# zbMATH — the first resource for mathematics

Compute Distance To:
 Author ID: voevodsky.vladimir-aleksandrovich Published as: Voevodsky, Vladimir; Voevodskij, V. A.; Voevodsky, V.; Voevodskiĭ, Vladimir Aleksandrovich; Voevodsky, V. A. Homepage: https://www.math.ias.edu/vladimir/home External Links: MacTutor · MGP · ORCID · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef Awards: Fields Medal (2002)
 Documents Indexed: 55 Publications since 1989, including 3 Books Biographic References: 10 Publications
all top 5

#### Co-Authors

 31 single-authored 6 Kapranov, Mikhail M. 5 Suslin, Andreĭ Aleksandrovich 3 Friedlander, Eric Mark 2 Ahrens, Benedikt 2 Lumsdaine, Peter LeFanu 2 Shabat, George B. 1 Awodey, Steve 1 Dundas, Bjørn Ian 1 Fiore, Marcelo P. 1 Garner, Richard 1 Kapulkin, Krzysztof 1 Levine, Marc Noel 1 Martin-Löf, Per 1 Mazza, Carlo 1 Morel, Fabien 1 Orlov, Dmitri O. 1 Østvær, Paul Arne 1 Pelayo, Alvaro 1 Röndigs, Oliver 1 Vishik, A. S. 1 Warren, Michael Alton 1 Weibel, Charles A.
all top 5

#### Serials

 4 Publications Mathématiques 4 Theory and Applications of Categories 3 Journal of Pure and Applied Algebra 2 Russian Mathematical Surveys 2 Cahiers de Topologie et Géométrie Différentielle Catégoriques 2 Mathematics of the USSR. Izvestiya 2 MSCS. Mathematical Structures in Computer Science 2 IMRN. International Mathematics Research Notices 2 Documenta Mathematica 2 Annals of Mathematics. Second Series 2 Journal of $$K$$-Theory 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Functional Analysis and its Applications 1 Inventiones Mathematicae 1 Proceedings of the American Mathematical Society 1 Soviet Mathematics. Doklady 1 Selecta Mathematica. New Series 1 Oberwolfach Reports 1 Annals of Mathematics Studies 1 Clay Mathematics Monographs 1 Logical Methods in Computer Science 1 Journal of Topology 1 Universitext
all top 5

#### Fields

 32 Algebraic geometry (14-XX) 22 Category theory; homological algebra (18-XX) 19 Algebraic topology (55-XX) 15 $$K$$-theory (19-XX) 13 Mathematical logic and foundations (03-XX) 6 Computer science (68-XX) 3 Convex and discrete geometry (52-XX) 2 Number theory (11-XX) 2 Field theory and polynomials (12-XX) 2 Group theory and generalizations (20-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX)

#### Citations contained in zbMATH Open

52 Publications have been cited 1,936 times in 963 Documents Cited by Year
$$\mathbb{A}^1$$-homotopy theory of schemes. Zbl 0983.14007
1999
Triangulated categories of motives over a field. Zbl 1019.14009
2000
Motivic cohomology with $$\mathbb Z/2$$-coefficients. Zbl 1057.14028
2003
Lecture notes on motivic cohomology. Zbl 1115.14010
Mazza, Carlo; Voevodsky, Vladimir; Weibel, Charles
2006
On motivic cohomology with $$\mathbb{Z}/l$$-coefficients. Zbl 1236.14026
2011
Bloch-Kato conjecture and motivic cohomology with finite coefficients. Zbl 1005.19001
2000
2-categories and Zamolodchikov tetrahedra equations. Zbl 0809.18006
Kapranov, M. M.; Voevodsky, V. A.
1994
$$\mathbb{A}^1$$-homotopy theory. Zbl 0907.19002
1998
Singular homology of abstract algebraic varieties. Zbl 0896.55002
1996
Reduced power operations in motivic cohomology. Zbl 1057.14027
2003
Cycles, transfers, and motivic homology theories. Zbl 1021.14006
Voevodsky, Vladimir; Suslin, Andrei; Friedlander, Eric M.
2000
An exact sequence for $$K^M_*/2$$ with applications to quadratic forms. Zbl 1124.14017
Orlov, D.; Vishik, A.; Voevodsky, V.
2007
Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic. Zbl 1057.14026
2002
Homology of schemes. Zbl 0871.14016
Voevodsky, V.
1996
Cohomological theory of presheaves with transfers. Zbl 1019.14010
2000
Relative cycles and Chow sheaves. Zbl 1019.14004
2000
Bivariant cycle cohomology. Zbl 1019.14011
2000
A nilpotence theorem for cycles algebraically equivalent to zero. Zbl 0861.14006
Voevodsky, V.
1995
Drawing curves over number fields. Zbl 0790.14026
Shabat, G. B.; Voevodskij, V. A.
1990
Open problems in the motivic stable homotopy theory. I. Zbl 1047.14012
2002
Braided monoidal 2-categories and Manin-Schechtman higher braid groups. Zbl 0791.18010
Kapranov, M.; Voevodsky, V.
1994
Motivic Eilenberg-MacLane spaces. Zbl 1227.14025
2010
Homotopy theory of simplicial sheaves in completely decomposable topologies. Zbl 1194.55020
2010
Unstable motivic homotopy categories in Nisnevich and cdh-topologies. Zbl 1187.14025
2010
Cancellation theorem. Zbl 1202.14022
2010
Free $$n$$-category generated by a cube, oriented matroids, and higher Bruhat orders. Zbl 0766.20005
Voevodskij, V. A.; Kapranov, M. M.
1991
Combinatorial-geometric aspects of polycategory theory: Pasting schemes and higher Bruhat orders (list of results). Zbl 0748.18010
Kapranov, M. M.; Voevodskij, V. A.
1991
On the zero slice of the sphere spectrum. Zbl 1182.14012
Voevodsky, V.
2004
A possible new approach to the motivic spectral sequence for algebraic $$K$$-theory. Zbl 1009.19003
2002
An experimental library of formalized mathematics based on the univalent foundations. Zbl 1361.68192
2015
Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields. Zbl 0697.14017
Voevodskij, V. A.; Shabat, G. B.
1989
Motives over simplicial schemes. Zbl 1194.14029
2010
A C-system defined by a universe category. Zbl 1436.03311
2015
Voevodsky’s Seattle lectures: $$K$$-theory and motivic cohomology. (Notes by C. Weibel). Zbl 0941.19001
Voevodsky, V.
1999
2010
$$\infty$$-groupoids and homotopy types. Zbl 0754.18008
Kapranov, M. M.; Voevodskij, V. A.
1991
Subsystems and regular quotients of C-systems. Zbl 1452.03040
2016
Products of families of types and $$(\Pi,\lambda)$$-structures on C-systems. Zbl 1380.03072
2016
Motivic homotopy theory. Lectures at a summer school in Nordfjordeid, Norway, August 2002. Zbl 1118.14001
Dundas, Bjørn Ian; Levine, Marc; Østvær, Paul Arne; Röndigs, Oliver; Voevodsky, V.
2007
C-systems defined by universe categories: presheaves. Zbl 1453.03067
2017
The $$(\Pi,\lambda)$$-structures on the C-systems defined by universe categories. Zbl 1383.03056
2017
Univalent foundations of mathematics. Zbl 1371.03097
2011
A univalent formalization of the $$p$$-adic numbers. Zbl 1361.68190
Pelayo, Álvaro; Voevodsky, Vladimir; Warren, Michael A.
2015
Galois representations connected with hyperbolic curves. Zbl 0770.14016
Voevodskij, V. A.
1991
Categorical structures for type theory in univalent foundations. Zbl 06943957
Ahrens, Benedikt; Lumsdaine, Peter Lefanu; Voevodsky, Vladimir
2018
Introduction. Zbl 1019.14008
Friedlander, Eric M.; Suslin, A.; Voevodsky, V.
2000
Mini-workshop: The homotopy interpretation of constructive type theory. Abstracts from the mini-workshop held February 27th-March 05th, 2011. Zbl 1242.00037
Awodey, Steve (ed.); Garner, Richard (ed.); Martin-Löf, Per (ed.); Voevodsky, Vladimir (ed.)
2011
Univalent semantics of constructive type theories. Zbl 1250.03121
2011
Étale topologies of schemes over fields of finite type over $$\mathbb{Q}$$. Zbl 0759.14012
Voevodskij, V. A.
1990
On Galois groups of function fields over fields of finite type over $$\mathbb{Q}$$. Zbl 0786.12004
Voevodskij, V. A.
1991
$$\infty$$-groupoids as a model for a homotopy category. Zbl 0721.55015
Voevodskij, V. A.; Kapranov, M. M.
1990
A cubical approach to straightening. Zbl 07311837
2020
A cubical approach to straightening. Zbl 07311837
2020
Categorical structures for type theory in univalent foundations. Zbl 06943957
Ahrens, Benedikt; Lumsdaine, Peter Lefanu; Voevodsky, Vladimir
2018
C-systems defined by universe categories: presheaves. Zbl 1453.03067
2017
The $$(\Pi,\lambda)$$-structures on the C-systems defined by universe categories. Zbl 1383.03056
2017
Subsystems and regular quotients of C-systems. Zbl 1452.03040
2016
Products of families of types and $$(\Pi,\lambda)$$-structures on C-systems. Zbl 1380.03072
2016
An experimental library of formalized mathematics based on the univalent foundations. Zbl 1361.68192
2015
A C-system defined by a universe category. Zbl 1436.03311
2015
A univalent formalization of the $$p$$-adic numbers. Zbl 1361.68190
Pelayo, Álvaro; Voevodsky, Vladimir; Warren, Michael A.
2015
On motivic cohomology with $$\mathbb{Z}/l$$-coefficients. Zbl 1236.14026
2011
Univalent foundations of mathematics. Zbl 1371.03097
2011
Mini-workshop: The homotopy interpretation of constructive type theory. Abstracts from the mini-workshop held February 27th-March 05th, 2011. Zbl 1242.00037
Awodey, Steve; Garner, Richard; Martin-Löf, Per; Voevodsky, Vladimir
2011
Univalent semantics of constructive type theories. Zbl 1250.03121
2011
Motivic Eilenberg-MacLane spaces. Zbl 1227.14025
2010
Homotopy theory of simplicial sheaves in completely decomposable topologies. Zbl 1194.55020
2010
Unstable motivic homotopy categories in Nisnevich and cdh-topologies. Zbl 1187.14025
2010
Cancellation theorem. Zbl 1202.14022
2010
Motives over simplicial schemes. Zbl 1194.14029
2010
2010
An exact sequence for $$K^M_*/2$$ with applications to quadratic forms. Zbl 1124.14017
Orlov, D.; Vishik, A.; Voevodsky, V.
2007
Motivic homotopy theory. Lectures at a summer school in Nordfjordeid, Norway, August 2002. Zbl 1118.14001
Dundas, Bjørn Ian; Levine, Marc; Østvær, Paul Arne; Röndigs, Oliver; Voevodsky, V.
2007
Lecture notes on motivic cohomology. Zbl 1115.14010
Mazza, Carlo; Voevodsky, Vladimir; Weibel, Charles
2006
On the zero slice of the sphere spectrum. Zbl 1182.14012
Voevodsky, V.
2004
Motivic cohomology with $$\mathbb Z/2$$-coefficients. Zbl 1057.14028
2003
Reduced power operations in motivic cohomology. Zbl 1057.14027
2003
Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic. Zbl 1057.14026
2002
Open problems in the motivic stable homotopy theory. I. Zbl 1047.14012
2002
A possible new approach to the motivic spectral sequence for algebraic $$K$$-theory. Zbl 1009.19003
2002
Triangulated categories of motives over a field. Zbl 1019.14009
2000
Bloch-Kato conjecture and motivic cohomology with finite coefficients. Zbl 1005.19001
2000
Cycles, transfers, and motivic homology theories. Zbl 1021.14006
Voevodsky, Vladimir; Suslin, Andrei; Friedlander, Eric M.
2000
Cohomological theory of presheaves with transfers. Zbl 1019.14010
2000
Relative cycles and Chow sheaves. Zbl 1019.14004
2000
Bivariant cycle cohomology. Zbl 1019.14011
2000
Introduction. Zbl 1019.14008
Friedlander, Eric M.; Suslin, A.; Voevodsky, V.
2000
$$\mathbb{A}^1$$-homotopy theory of schemes. Zbl 0983.14007
1999
Voevodsky’s Seattle lectures: $$K$$-theory and motivic cohomology. (Notes by C. Weibel). Zbl 0941.19001
Voevodsky, V.
1999
$$\mathbb{A}^1$$-homotopy theory. Zbl 0907.19002
1998
Singular homology of abstract algebraic varieties. Zbl 0896.55002
1996
Homology of schemes. Zbl 0871.14016
Voevodsky, V.
1996
A nilpotence theorem for cycles algebraically equivalent to zero. Zbl 0861.14006
Voevodsky, V.
1995
2-categories and Zamolodchikov tetrahedra equations. Zbl 0809.18006
Kapranov, M. M.; Voevodsky, V. A.
1994
Braided monoidal 2-categories and Manin-Schechtman higher braid groups. Zbl 0791.18010
Kapranov, M.; Voevodsky, V.
1994
Free $$n$$-category generated by a cube, oriented matroids, and higher Bruhat orders. Zbl 0766.20005
Voevodskij, V. A.; Kapranov, M. M.
1991
Combinatorial-geometric aspects of polycategory theory: Pasting schemes and higher Bruhat orders (list of results). Zbl 0748.18010
Kapranov, M. M.; Voevodskij, V. A.
1991
$$\infty$$-groupoids and homotopy types. Zbl 0754.18008
Kapranov, M. M.; Voevodskij, V. A.
1991
Galois representations connected with hyperbolic curves. Zbl 0770.14016
Voevodskij, V. A.
1991
On Galois groups of function fields over fields of finite type over $$\mathbb{Q}$$. Zbl 0786.12004
Voevodskij, V. A.
1991
Drawing curves over number fields. Zbl 0790.14026
Shabat, G. B.; Voevodskij, V. A.
1990
Étale topologies of schemes over fields of finite type over $$\mathbb{Q}$$. Zbl 0759.14012
Voevodskij, V. A.
1990
$$\infty$$-groupoids as a model for a homotopy category. Zbl 0721.55015
Voevodskij, V. A.; Kapranov, M. M.
1990
Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields. Zbl 0697.14017
Voevodskij, V. A.; Shabat, G. B.
1989
all top 5

#### Cited by 741 Authors

 26 Østvær, Paul Arne 21 Panin, Ivan A. 16 Levine, Marc Noel 15 Voevodskiĭ, Vladimir Aleksandrovich 14 Tabuada, Gonçalo 14 Weibel, Charles A. 14 Yagita, Nobuaki 13 Kahn, Bruno 13 Mináč, Ján 12 Asok, Aravind 12 Isaksen, Daniel C. 11 Déglise, Frédéric 11 Krishna, Amalendu 11 Laterveer, Robert 10 Fasel, Jean 10 Ormsby, Kyle M. 10 Röndigs, Oliver 10 Walker, Mark E. 9 Bondarko, Mikhail Vladimirovich 9 Friedlander, Eric Mark 9 Garkusha, Grigory 9 Gille, Stefan G. 9 Hasemeyer, Christian 9 Heller, Jeremiah 8 Ananyevskiy, Alexey 8 Ayoub, Joseph 8 Dugger, Daniel 8 Geisser, Thomas H. 8 Hoyois, Marc 8 Voisin, Claire 8 Wickelgren, Kirsten G. 7 Binda, Federico 7 Ivorra, Florian 7 Marcolli, Matilde 7 Rosenschon, Andreas 7 Wendt, Matthias 6 Hornbostel, Jens 6 Kerz, Moritz C. 6 Kuniba, Atsuo 6 Nguyêñ Duy Tân 6 Pelaez, Pablo 6 Saito, Shuji 6 Schmidt, Alexander 6 Spitzweck, Markus 6 Williams, Ben 6 Yamazaki, Takao 5 Ahrens, Benedikt 5 Bachmann, Tom 5 Becher, Karim Johannes 5 Choudhury, Utsav 5 Cortiñas, Guillermo H. 5 Druzhinin, Andreĭ É. 5 Elgueta, Josep 5 Guletskiǐ, Vladimir 5 Huber-Klawitter, Annette 5 Kapranov, Mikhail M. 5 Merkur’ev, Aleksandr Sergeevich 5 Morel, Fabien 5 Positselski, Leonid Efimovich 5 Rülling, Kay 5 Scholbach, Jakob 5 Suslin, Andreĭ Aleksandrovich 5 Vezzani, Alberto 5 Vishik, Alexander 4 Baez, John C. 4 Barbieri Viale, Luca 4 Cegarra, Antonio Martínez 4 Cisinski, Denis-Charles 4 Crane, Louis 4 Crans, Sjoerd E. 4 Guillou, Bertrand J. 4 Hill, Michael A. 4 Itzykson, Claude 4 Karoubi, Max 4 Karpenko, Nikita Aleksandrovich 4 Kelly, Shane 4 Kondo, Satoshi 4 Kříž, Igor 4 Lumsdaine, Peter LeFanu 4 Matzri, Eliyahu 4 Neshitov, Alexander 4 Okado, Masato 4 Park, Jinhyun 4 Quadrelli, Claudio 4 Quick, Gereon 4 Sato, Kanetomo 4 Shabat, George B. 4 Szabo, Richard J. 4 Vezzosi, Gabriele 4 Voineagu, Mircea Alexandru 4 Yasuda, Seidai 4 Yetter, David N. 3 Akhtar, Reza 3 Berrick, A. Jon 3 Bhatt, Bhargav 3 Biglari, Shahram 3 Borghesi, Simone 3 Carrasco, Pilar C. 3 Carter, J. Scott 3 Chebolu, Sunil K. ...and 641 more Authors
all top 5

#### Cited in 166 Serials

 86 Advances in Mathematics 72 Journal of Pure and Applied Algebra 34 Journal of Algebra 33 Transactions of the American Mathematical Society 32 Journal of $$K$$-Theory 27 Compositio Mathematica 25 Mathematische Annalen 22 Documenta Mathematica 18 Mathematische Zeitschrift 18 Algebraic & Geometric Topology 17 Duke Mathematical Journal 17 Inventiones Mathematicae 17 Journal of Number Theory 16 Comptes Rendus. Mathématique. Académie des Sciences, Paris 16 Journal of the Institute of Mathematics of Jussieu 15 Manuscripta Mathematica 14 Communications in Mathematical Physics 14 Journal of Algebraic Geometry 14 Journal of Mathematical Sciences (New York) 14 Geometry & Topology 13 Proceedings of the American Mathematical Society 13 $$K$$-Theory 13 Applied Categorical Structures 13 Selecta Mathematica. New Series 12 St. Petersburg Mathematical Journal 11 Journal of Homotopy and Related Structures 10 Annals of Mathematics. Second Series 8 Publications Mathématiques 8 Journal of the American Mathematical Society 8 Journal of the European Mathematical Society (JEMS) 7 Journal of Mathematical Physics 7 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 7 Journal für die Reine und Angewandte Mathematik 7 Rendiconti del Seminario Matematico della Università di Padova 7 Bulletin of the American Mathematical Society. New Series 7 Forum of Mathematics, Sigma 6 Communications in Algebra 6 Annales de l’Institut Fourier 6 Research in the Mathematical Sciences 5 Theoretical and Mathematical Physics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Cahiers de Topologie et Géométrie Différentielle Catégoriques 5 Topology and its Applications 5 Journal of High Energy Physics 5 International Journal of Number Theory 5 Journal of Topology 5 Annals of $$K$$-Theory 4 Letters in Mathematical Physics 4 Bulletin of the London Mathematical Society 4 Functional Analysis and its Applications 4 Journal of Combinatorial Theory. Series A 4 Journal of the Mathematical Society of Japan 4 Nagoya Mathematical Journal 4 International Journal of Mathematics 4 Journal of Knot Theory and its Ramifications 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Discrete Mathematics 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Canadian Journal of Mathematics 3 Tohoku Mathematical Journal. Second Series 3 Theory and Applications of Categories 3 Transformation Groups 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Algebra & Number Theory 3 Japanese Journal of Mathematics. 3rd Series 2 Mathematical Notes 2 Nuclear Physics. B 2 Russian Mathematical Surveys 2 Collectanea Mathematica 2 Commentarii Mathematici Helvetici 2 Geometriae Dedicata 2 International Journal of Mathematics and Mathematical Sciences 2 Kodai Mathematical Journal 2 Mathematische Nachrichten 2 Memoirs of the American Mathematical Society 2 Michigan Mathematical Journal 2 Pacific Journal of Mathematics 2 European Journal of Combinatorics 2 Forum Mathematicum 2 Sugaku Expositions 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Expositiones Mathematicae 2 Indagationes Mathematicae. New Series 2 Vestnik St. Petersburg University. Mathematics 2 Journal of Algebraic Combinatorics 2 Annales Mathématiques Blaise Pascal 2 The New York Journal of Mathematics 2 Sbornik: Mathematics 2 Izvestiya: Mathematics 2 Communications in Contemporary Mathematics 2 Lobachevskii Journal of Mathematics 2 Proceedings of the Steklov Institute of Mathematics 2 Journal of Noncommutative Geometry 2 Logical Methods in Computer Science 2 Journal of Singularities 2 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 2 Kyoto Journal of Mathematics 2 European Journal of Mathematics 2 Journal de l’École Polytechnique – Mathématiques ...and 66 more Serials
all top 5

#### Cited in 40 Fields

 623 Algebraic geometry (14-XX) 291 $$K$$-theory (19-XX) 215 Algebraic topology (55-XX) 212 Category theory; homological algebra (18-XX) 155 Number theory (11-XX) 79 Group theory and generalizations (20-XX) 56 Associative rings and algebras (16-XX) 56 Manifolds and cell complexes (57-XX) 49 Field theory and polynomials (12-XX) 48 Quantum theory (81-XX) 37 Commutative algebra (13-XX) 27 Nonassociative rings and algebras (17-XX) 26 Mathematical logic and foundations (03-XX) 26 Several complex variables and analytic spaces (32-XX) 22 Combinatorics (05-XX) 16 Convex and discrete geometry (52-XX) 12 Differential geometry (53-XX) 12 Global analysis, analysis on manifolds (58-XX) 12 Computer science (68-XX) 11 Dynamical systems and ergodic theory (37-XX) 8 Functions of a complex variable (30-XX) 7 Topological groups, Lie groups (22-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 6 Relativity and gravitational theory (83-XX) 5 General and overarching topics; collections (00-XX) 5 History and biography (01-XX) 5 Partial differential equations (35-XX) 5 Functional analysis (46-XX) 4 Special functions (33-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Measure and integration (28-XX) 3 Geometry (51-XX) 3 General topology (54-XX) 2 General algebraic systems (08-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Mechanics of particles and systems (70-XX)

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.