×

Vladimir Voevodsky, Fields Medal 2002. (Vladimir Voevodsky, Medalla Fields 2002.) (Spanish) Zbl 1485.01060

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
14C15 (Equivariant) Chow groups and rings; motives
14F42 Motivic cohomology; motivic homotopy theory

Biographic References:

Voevodsky, Vladimir
PDF BibTeX XML Cite
Full Text: Link

References:

[1] B. Ahrens, P. L. Lumsdaine y V. Voevodsky, Categorical structures for type theory in univalent foundations,Computer science logic 2017, Art. No. 8, LIPIcs. Leibniz Int. Proc. Inform.82, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2017. · Zbl 07204300
[2] J. Ayoub, Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique. I,Astérisque314(2007). · Zbl 1146.14001
[3] J. Ayoub, Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique. II,Astérisque315(2007). · Zbl 1146.14001
[4] A. Bauer, J. Gross, P. L. Lumsdaine, M. Shulman, M. Sozeau y B. Spitters, The HoTT Library: A formalization of homotopy type theory inCoq, Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs, 164-172, 2017.
[5] A. Beilinson, Height pairing between algebraic cycles,K-theory, arithmetic and geometry (Moscow, 1984-1986), 1-25, Lecture Notes in Math.1289, Springer, Berlin, 1987.
[6] A. Beilinson, Remarks on Grothendieck’s standard conjectures,Regulators, 25-32, Contemp. Math.,571, Amer. Math. Soc., Providence, RI, 2012. · Zbl 1268.14007
[7] A. Beilinson, R. MacPherson y V. Schechtman, Notes on motivic cohomology,Duke Math. J.54(1987), no. 2, 679-710. · Zbl 0632.14010
[8] S. Bloch, Algebraic cycles and higherK-theory,Adv. in Math.61(1986), no. 3, 267-304. · Zbl 0608.14004
[9] S. Bloch, The moving lemma for higher Chow groups,J. Algebraic Geom.3 (1994), 537-568. · Zbl 0830.14003
[10] S. Bloch y K. Kato,p-adic étale cohomology,Inst. Hautes Études Sci. Publ. Math., No. 63 (1986), 107-152. · Zbl 0613.14017
[11] G. Brunerie et al.Homotopy Type Theory in Agda, an Agda library of formalized proofs,disponible enhttps://github.com/HoTT/HoTT-Agda
[12] Coq Platform, The HoTT Library, a Coq library of formalized proofs,disponible enhttps://github.com/HoTT/HoTT
[13] P. Deligne, Carta a C. Soulé, 1985.
[14] P. Deligne, Le groupe fondamental de la droite projective moins trois points, Galois groups overQ(Berkeley, CA, 1987), 79-297,Math. Sci. Res. Inst. Publ. 16, Springer, New York-Berlin, 1989. · Zbl 0742.14022
[15] P. Deligne, Voevodsky’s Lectures on Motivic Cohomology 2000/2001,Algebraic topology, 355-409,Abel Symp.4, Springer, Berlin, 2009. · Zbl 1183.14028
[16] D. Grayson, An introduction to univalent foundations for mathematicians, Bull. Amer. Math. Soc. (N.S.)55(2018), no. 4, 427-450. · Zbl 1461.03012
[17] A. Grothendieck, Pursuing stacks,manuscrito(1983), por aparecer enDoc. Math..
[18] M. Hanamura, Mixed motives and algebraic cycles I,Math. Res. Lett.2 (1995), no. 6, 811-821. · Zbl 0867.14003
[19] M. Hanamura, Mixed motives and algebraic cycles III,Math. Res. Lett.6 (1999), no. 1, 61-82. · Zbl 0968.14004
[20] M. Hanamura, Mixed motives and algebraic cycles II,Invent. Math.158 (2004), no. 1, 105-179. · Zbl 1068.14022
[21] S. Henry, What is the mistake in the proof of the Homotopy hypothesis by Kapranov and Voevodsky?,MathOverflow,https://mathoverflow.net/ q/234492(versión: 2017-11-29).
[22] B. Kahn, La conjecture de Milnor (d’après V. Voevodsky),Handbook of Ktheory1,2, 1105-1149, Springer, Berlin, 2005. · Zbl 1101.19001
[23] M. Kapranov y V. Voevodsky, The freen-category generated by a cube, oriented matroids and higher Bruhat orders,Funktsional. Anal. i Prilozhen.25 (1991), 62-65. Versión en inglés:Funct. Anal. Appl.25(1991), no. 1, 50-52. · Zbl 0766.20005
[24] M. Kapranov y V. Voevodsky,∞-groupoids and homotopy types,International Category Theory Meeting (Bangor, 1989 and Cambridge, 1990). Cahiers Topologie Géom. Différentielle Catég.32(1991), 29-46.
[25] M. Kapranov y V. Voevodsky, Combinatorial geometric aspects of polycategory theory: pasting schemes and higher Bruhat orders (list of results), International Category Theory Meeting (Bangor, 1989 and Cambridge, 1990). Cahiers Topologie Géom. Différentielle Catég.32(1991), 11-27. · Zbl 0748.18010
[26] K. Kapulkin y P. L. Lumsdaine, The simplicial model of univalent foundations (after Voevodsky),J. Eur. Math. Soc. (JEMS)23(2021), no. 6, 2071- 2126. · Zbl 1471.18025
[27] M. Levine,Mixed motives, Mathematical Surveys and Monographs57, American Mathematical Society, Providence, RI, 1998. · Zbl 0902.14003
[28] M. Levine, Mixed motives,Handbook of K-theory, vol. I, 429-521, Springer, Berlin, 2005. · Zbl 1112.14020
[29] S. Lichtenbaum, Values of zeta functions at non-negative integers,Number theory (Noordwijkerhout, 1983), 127-138, Lecture Notes in Math.1068, Springer, Berlin, 1984. · Zbl 0591.14014
[30] C. Mazza, V. Voevodsky y C. Weibel,Lecture notes on motivic cohomology, Clay Mathematics Monographs,2, American Mathematical Society, Providence, RI, 2006. · Zbl 1115.14010
[31] J. S. Milne, Motives—Grothendieck’s dream,Open problems and surveys of contemporary mathematics, Int. Press, Somerville, MA,6(2013), 325-342. · Zbl 1314.14010
[32] J. Milnor, AlgebraicK-theory and quadratic forms,Invent. Math.9(1970), 318-344. · Zbl 0199.55501
[33] F. Morel y V. Voevodsky,A1-homotopy theory of schemes,Inst. Hautes Études Sci. Publ. Math.90(1999), 45-143 (2001). · Zbl 0983.14007
[34] D. Orlov, A. Vishik y V. Voevodsky, An exact sequence forK∗M/2 with applications to quadratic forms,Ann. of Math. (2)165(2007), no. 1, 1-13. · Zbl 1124.14017
[35] J. Riou, La conjecture de Bloch-Kato (d’après M. Rost et V. Voevodsky), Astérisque361(2014), 421-463. · Zbl 1366.19001
[36] G. Shabat y V. Voevodsky, Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields,Dokl. Akad. Nauk SSSR304(1989), 265-268. Versión en inglés:Soviet Math. Dokl.39(1989), no. 1, 38-41. · Zbl 0697.14017
[37] G. Shabat y V. Voevodsky, Drawing Curves over Number Fields,The Grothendieck Festschrift, Vol. III, 199-227,Progr. Math.88, Birkhäuser Boston, Boston, MA, 1990. · Zbl 0790.14026
[38] C. Simpson, Homotopy types of strict 3-groupoids,disponible enhttps:// arxiv.org/abs/math/9810059
[39] TheUnivalentFoundationsProgram,HomotopyTypeTheory: UnivalentFoundationsofMathematics,2013,disponible enhttps:// homotopytypetheory.org/book/
[40] V. Voevodsky, Étale topologies of schemes over fields of finite type overQ, Izv. Akad. Nauk SSSR Ser. Mat.54(1990), no. 6, 1155-1167. Versión en inglés: Math. USSR-Izv.37(1991), no. 3, 511-523. · Zbl 0759.14012
[41] V. Voevodsky, Galois groups of function fields over fields of finite type overQ, Uspekhi Mat. Nauk46(1991), no. 5(281), 163-164. Versión en inglés:Russian Math. Surveys46(1991), no. 5, 202-203. · Zbl 0786.12004
[42] V. Voevodsky, Galois representations connected with hyperbolic curves,Izv. Akad. Nauk SSSR Ser. Mat.55(1991), no. 6, 1331-1342. Versión en inglés: Math. USSR-Izv.39(1992), no. 3, 1281-1291. · Zbl 0770.14016
[43] V. Voevodsky, Homology of schemes,Selecta Math. (N.S.)2(1996), no. 1, 111-153. · Zbl 0871.14016
[44] V. Voevodsky,A1-homotopy theory,Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998),Doc. Math.1998, Extra Vol. I, 579-604. · Zbl 0907.19002
[45] V. Voevodskyy, Reduced power operations in motivic cohomology,Publ. Math. Inst. Hautes Études Sci.98(2003), 1-57. · Zbl 1057.14027
[46] V. Voevodsky, Motivic cohomology withZ/2-coefficients,Publ. Math. Inst. Hautes Études Sci.98(2003), 59-104. · Zbl 1057.14028
[47] V. Voevodsky, Cancellation theorem,Doc. Math.2010 (Extra volume: A. Suslin sixtieth birthday), 671-685. · Zbl 1202.14022
[48] V. Voevodsky, Motivic Eilenberg-Maclane spaces,Publ. Math. Inst. Hautes Études Sci.112(2010), 1-99. · Zbl 1227.14025
[49] V. Voevodsky, Motives over simplicial schemes,J.K-theory5(2010), 1-38. · Zbl 1194.14029
[50] V. Voevodsky, Simplicial radditive functors,J.K-theory5(2010), 201-244. · Zbl 1194.55021
[51] V. Voevodsky, Unstable motivic homotopy categories in Nisnevich andcdhtopologies,J. Pure Appl. Algebra214(2010), 1399-1406. · Zbl 1187.14025
[52] V. Voevodsky, Homotopy theory of simplicial sheaves in completely decomposable topologies,J. Pure Appl. Algebra214(2010), 1384-1398. · Zbl 1194.55020
[53] V. Voevodsky, On motivic cohomology withZ/l-coefficients,Ann. of Math. (2)174(2011), no. 1, 401-438. · Zbl 1236.14026
[54] V. Voevodsky, An experimental library of formalized mathematics based on the univalent foundations,Math. Structures Comput. Sci.25(2015), no. 5, 1278-1294. · Zbl 1361.68192
[55] V. Voevodsky, B. Ahrens, D. Grayson et al.,UniMath — a computerchecked library of univalent mathematics, disponible enhttp://UniMath.org
[56] V. Voevodsky y M. Kapranov,∞-groupoids as a model for a homotopy category,Uspekhi Mat. Nauk45(1990), no. 5(275), 183-184. Versión en inglés: Russian Math. Surveys45(1990), no. 5, 239-240. · Zbl 0721.55015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.