Edit Profile (opens in new tab) Spivakovsky, Mark Co-Author Distance Author ID: spivakovsky.mark Published as: Spivakovsky, Mark; Spivakovsky, M. External Links: MGP · Wikidata · IdRef · theses.fr Documents Indexed: 47 Publications since 1982 2 Contributions as Editor · 1 Further Contribution Co-Authors: 36 Co-Authors with 36 Joint Publications 440 Co-Co-Authors all top 5 Co-Authors 12 single-authored 6 Arimoto, Shigeru 5 Lucas, François 5 Schaub, Daniel 5 Taylor, Keith Frederick 4 Mezey, Paul G. 4 Novacoski, Josnei 3 Herrera Govantes, Francisco Javier 3 Mahboub, Wael 3 Olalla-Acosta, Miguel Ángel 3 Plénat, Camille 2 Beddani, Charef 2 Cano, Felipe 2 El Khoury, Antoine C. 2 Madden, James J. 2 Méhats, Laurent 2 Solov’ëv, Sergeĭ Vladimirovich 2 Teissier, Bernard 2 Yoshida, Eiji 1 Amini, Massoud 1 Barnabé, M. S. 1 Decaup, Julie 1 Dotsenko, Vladimir Viktorovich 1 Fernández de Bobadilla, Javier 1 Grigor’ev, Dmitriĭ Yur’evich 1 Leyton-Alvarez, Maximiliano 1 Loray, Frank 1 Milman, Pierre D. 1 Morales-Ruiz, Juan José 1 Mourtada, Hussein 1 Novacoski, J. A. 1 Roche, Claude Andre 1 Rond, Guillaume 1 Sad, Paulo Roberto 1 Shen, Alexander 1 Silva de Souza, C. H. 1 Snoussi, Jawad 1 Yamabe, Tokio 1 Yokotani, Masaaki all top 5 Serials 6 Journal of Algebra 6 Journal of Mathematical Chemistry 3 Journal of Pure and Applied Algebra 2 Michigan Mathematical Journal 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Advances in Mathematics 1 American Journal of Mathematics 1 Compositio Mathematica 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Kodai Mathematical Journal 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Proceedings of the London Mathematical Society. Third Series 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal of Mathematical Sciences (New York) 1 European Mathematical Society Newsletter 1 Annals of Mathematics. Second Series 1 Astérisque 1 Journal of Singularities 1 Arnold Mathematical Journal all top 5 Fields 27 Algebraic geometry (14-XX) 22 Commutative algebra (13-XX) 7 Field theory and polynomials (12-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Biology and other natural sciences (92-XX) 3 Convex and discrete geometry (52-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Quantum theory (81-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Category theory; homological algebra (18-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Functional analysis (46-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 35 Publications have been cited 364 times in 272 Documents Cited by ▼ Year ▼ Valuations in function fields of surfaces. Zbl 0716.13003Spivakovsky, Mark 94 1990 Sandwiched singularities and desingularization of surfaces by normalized Nash transformations. Zbl 0719.14005Spivakovsky, Mark 56 1990 A new proof of D. Popescu’s theorem on smoothing of ring homomorphisms. Zbl 0919.13009Spivakovsky, Mark 42 1999 Key polynomials and pseudo-convergent sequences. Zbl 1391.13009Novacoski, Josnei; Spivakovsky, Mark 22 2018 Valuations in algebraic field extensions. Zbl 1170.12002Herrera Govantes, F. J.; Olalla Acosta, M. A.; Spivakovsky, M. 19 2007 Abstract key polynomials and comparison theorems with the key polynomials of Mac Lane-Vaquié. Zbl 1432.12001Decaup, J.; Mahboub, W.; Spivakovsky, M. 14 2018 Extending a valuation centred in a local domain to the formal completion. Zbl 1276.12004Herrera Govantes, F. J.; Olalla Acosta, M. A.; Spivakovsky, M.; Teissier, B. 13 2012 Nash resolution for binomial varieties as Euclidean division. A priori termination bound, polynomial complexity in essential dimension 2. Zbl 1287.14004Grigoriev, Dima; Milman, Pierre D. 12 2012 Reduction of singularities of three-dimensional line foliations. Zbl 1346.14038Cano, F.; Roche, C.; Spivakovsky, M. 10 2014 Proof of the Fukui conjecture via resolution of singularities and related methods. I. Zbl 1068.92048Arimoto, Shigeru; Spivakovsky, Mark; Taylor, Keith F.; Mezey, Paul G. 10 2005 A solution to Hironaka’s polyhedra game. Zbl 0531.14009Spivakovsky, Mark 9 1983 On connectedness of sets in the real spectra of polynomial rings. Zbl 1169.14039Lucas, F.; Madden, J. J.; Schaub, D.; Spivakovsky, M. 7 2009 Proof of the Fukui conjecture via resolution of singularities and related methods. II. Zbl 1075.92055Arimoto, Shigeru; Spivakovsky, Mark; Taylor, Keith F.; Mezey, Paul G. 7 2005 Non-existence of the Artin function for Henselian pairs. Zbl 0803.13005Spivakovsky, Mark 6 1994 Valuations, the linear Artin approximation theorem and convergence of formal functions. Zbl 0747.13004Spivakovsky, Mark 5 1990 Approximate roots of a valuation and the Pierce-Birkhoff conjecture. Zbl 1271.13051Lucas, F.; Madden, J.; Schaub, D.; Spivakovsky, M. 5 2012 The Nash problem of arcs and the rational double point \(E_{6}\). Zbl 1271.14006Plénat, Camille; Spivakovsky, Mark 5 2012 On common extensions of valued fields. Zbl 1486.12007Mahboub, W.; Mansour, A.; Spivakovsky, M. 5 2021 The analogue of Izumi’s theorem for Abhyankar valuations. Zbl 1318.13007Rond, G.; Spivakovsky, M. 4 2014 Reduction of local uniformization to the rank one case. Zbl 1312.13010Novacoski, Josnei; Spivakovsky, Mark 4 2014 Proof of the Fukui conjecture via resolution of singularities and related methods. IV. Zbl 1262.92072Arimoto, Shigeru; Spivakovsky, Mark; Taylor, Keith F.; Mezey, Paul G. 3 2010 Proof of the Fukui conjecture via resolution of singularities and related methods. V. Zbl 1262.92073Arimoto, Shigeru; Spivakovsky, Mark; Yoshida, Eiji; Taylor, Keith F.; Mezey, Paul G. 3 2011 A counterexample to Hironaka’s ”hard” polyhedra game. Zbl 0531.14010Spivakovsky, Mark 2 1982 A counterexample to the theorem of Beppo Levi in three dimensions. Zbl 0688.14012Spivakovsky, Mark 2 1989 On the local uniformization problem. Zbl 1346.13048Novacoski, Josnei; Spivakovsky, Mark 2 2016 Sandwiched surface singularities and the Nash resolution problem. Zbl 0626.14012Spivakovsky, Mark 2 1987 Equisingularity in one-parameter families of generically reduced curves. Zbl 1405.32042Fernández de Bobadilla, J.; Snoussi, J.; Spivakovsky, M. 2 2017 The Nash problem and its solution: a survey. Zbl 1327.14021Plénat, Camille; Spivakovsky, Mark 2 2015 Resolution of singularities: an introduction. Zbl 1477.14025Spivakovsky, Mark 2 2020 Reduction of local uniformization to the case of rank one valuations for rings with zero divisors. Zbl 1372.13003Novacoski, Josnei; Spivakovsky, Mark 2 2017 On the structure of the graded algebra associated to a valuation. Zbl 1440.13023Barnabé, M. S.; Novacoski, J.; Spivakovsky, M. 1 2020 Graded rings associated to valuations and direct limits. Zbl 1509.13011Silva de Souza, C. H.; Novacoski, J. A.; Spivakovsky, M. 1 2023 On the Pierce-Birkhoff conjecture. Zbl 1386.14197Lucas, F.; Schaub, D.; Spivakovsky, M. 1 2015 Repeat space theory applied to carbon nanotubes and related molecular networks. III. Zbl 1402.92442Arimoto, Shigeru; Spivakovsky, Mark; Amini, Massoud; Yoshida, Eiji; Yokotani, Masaaki; Yamabe, Tokio 1 2012 Generalization of a result of Hickel, Ito and Izumi about a Diophantine inequality. Zbl 1310.13015Beddani, Charef; Spivakovsky, Mark 1 2015 Graded rings associated to valuations and direct limits. Zbl 1509.13011Silva de Souza, C. H.; Novacoski, J. A.; Spivakovsky, M. 1 2023 On common extensions of valued fields. Zbl 1486.12007Mahboub, W.; Mansour, A.; Spivakovsky, M. 5 2021 Resolution of singularities: an introduction. Zbl 1477.14025Spivakovsky, Mark 2 2020 On the structure of the graded algebra associated to a valuation. Zbl 1440.13023Barnabé, M. S.; Novacoski, J.; Spivakovsky, M. 1 2020 Key polynomials and pseudo-convergent sequences. Zbl 1391.13009Novacoski, Josnei; Spivakovsky, Mark 22 2018 Abstract key polynomials and comparison theorems with the key polynomials of Mac Lane-Vaquié. Zbl 1432.12001Decaup, J.; Mahboub, W.; Spivakovsky, M. 14 2018 Equisingularity in one-parameter families of generically reduced curves. Zbl 1405.32042Fernández de Bobadilla, J.; Snoussi, J.; Spivakovsky, M. 2 2017 Reduction of local uniformization to the case of rank one valuations for rings with zero divisors. Zbl 1372.13003Novacoski, Josnei; Spivakovsky, Mark 2 2017 On the local uniformization problem. Zbl 1346.13048Novacoski, Josnei; Spivakovsky, Mark 2 2016 The Nash problem and its solution: a survey. Zbl 1327.14021Plénat, Camille; Spivakovsky, Mark 2 2015 On the Pierce-Birkhoff conjecture. Zbl 1386.14197Lucas, F.; Schaub, D.; Spivakovsky, M. 1 2015 Generalization of a result of Hickel, Ito and Izumi about a Diophantine inequality. Zbl 1310.13015Beddani, Charef; Spivakovsky, Mark 1 2015 Reduction of singularities of three-dimensional line foliations. Zbl 1346.14038Cano, F.; Roche, C.; Spivakovsky, M. 10 2014 The analogue of Izumi’s theorem for Abhyankar valuations. Zbl 1318.13007Rond, G.; Spivakovsky, M. 4 2014 Reduction of local uniformization to the rank one case. Zbl 1312.13010Novacoski, Josnei; Spivakovsky, Mark 4 2014 Extending a valuation centred in a local domain to the formal completion. Zbl 1276.12004Herrera Govantes, F. J.; Olalla Acosta, M. A.; Spivakovsky, M.; Teissier, B. 13 2012 Nash resolution for binomial varieties as Euclidean division. A priori termination bound, polynomial complexity in essential dimension 2. Zbl 1287.14004Grigoriev, Dima; Milman, Pierre D. 12 2012 Approximate roots of a valuation and the Pierce-Birkhoff conjecture. Zbl 1271.13051Lucas, F.; Madden, J.; Schaub, D.; Spivakovsky, M. 5 2012 The Nash problem of arcs and the rational double point \(E_{6}\). Zbl 1271.14006Plénat, Camille; Spivakovsky, Mark 5 2012 Repeat space theory applied to carbon nanotubes and related molecular networks. III. Zbl 1402.92442Arimoto, Shigeru; Spivakovsky, Mark; Amini, Massoud; Yoshida, Eiji; Yokotani, Masaaki; Yamabe, Tokio 1 2012 Proof of the Fukui conjecture via resolution of singularities and related methods. V. Zbl 1262.92073Arimoto, Shigeru; Spivakovsky, Mark; Yoshida, Eiji; Taylor, Keith F.; Mezey, Paul G. 3 2011 Proof of the Fukui conjecture via resolution of singularities and related methods. IV. Zbl 1262.92072Arimoto, Shigeru; Spivakovsky, Mark; Taylor, Keith F.; Mezey, Paul G. 3 2010 On connectedness of sets in the real spectra of polynomial rings. Zbl 1169.14039Lucas, F.; Madden, J. J.; Schaub, D.; Spivakovsky, M. 7 2009 Valuations in algebraic field extensions. Zbl 1170.12002Herrera Govantes, F. J.; Olalla Acosta, M. A.; Spivakovsky, M. 19 2007 Proof of the Fukui conjecture via resolution of singularities and related methods. I. Zbl 1068.92048Arimoto, Shigeru; Spivakovsky, Mark; Taylor, Keith F.; Mezey, Paul G. 10 2005 Proof of the Fukui conjecture via resolution of singularities and related methods. II. Zbl 1075.92055Arimoto, Shigeru; Spivakovsky, Mark; Taylor, Keith F.; Mezey, Paul G. 7 2005 A new proof of D. Popescu’s theorem on smoothing of ring homomorphisms. Zbl 0919.13009Spivakovsky, Mark 42 1999 Non-existence of the Artin function for Henselian pairs. Zbl 0803.13005Spivakovsky, Mark 6 1994 Valuations in function fields of surfaces. Zbl 0716.13003Spivakovsky, Mark 94 1990 Sandwiched singularities and desingularization of surfaces by normalized Nash transformations. Zbl 0719.14005Spivakovsky, Mark 56 1990 Valuations, the linear Artin approximation theorem and convergence of formal functions. Zbl 0747.13004Spivakovsky, Mark 5 1990 A counterexample to the theorem of Beppo Levi in three dimensions. Zbl 0688.14012Spivakovsky, Mark 2 1989 Sandwiched surface singularities and the Nash resolution problem. Zbl 0626.14012Spivakovsky, Mark 2 1987 A solution to Hironaka’s polyhedra game. Zbl 0531.14009Spivakovsky, Mark 9 1983 A counterexample to Hironaka’s ”hard” polyhedra game. Zbl 0531.14010Spivakovsky, Mark 2 1982 all cited Publications top 5 cited Publications all top 5 Cited by 234 Authors 22 Spivakovsky, Mark 17 Galindo Pastor, Carlos 16 Cutkosky, Steven Dale 10 Arimoto, Shigeru 8 Monserrat, Francisco 8 Novacoski, Josnei 8 Pichon, Anne 8 Popescu, Dorin 8 Rond, Guillaume 6 Bilski, Marcin 6 Duarte, Daniel C. S. 6 Fernández-Sánchez, Jesús 6 Nart, Enric 6 Piltant, Olivier 5 Granja, Angel 5 Kashcheyeva, Olga 5 Lucas, François 5 Mourtada, Hussein 5 Schaub, Daniel 4 Bishnoi, Anuj 4 Campillo, Antonio 4 Cano, Felipe 4 Cossart, Vincent 4 Dutta, Arpan 4 Fantini, Lorenzo 4 Hauser, Herwig 4 Jonsson, Mattias 4 Martínez, Ma. Carmen 4 Mavi, Sneha 4 Moyano Fernández, Julio José 4 Pedersen, Helge Møller 4 Pfister, Gerhard 4 Rodríguez, Cristina 4 Teissier, Bernard 3 Alberich-Carramiñana, Maria 3 Belotto da Silva, André Ricardo 3 Chávez Martínez, Enrique 3 de Felipe, Ana Belén 3 Delgado, Felix 3 ElHitti, Samar 3 Favre, Charles 3 Fedorov, Roman M. 3 Ghezzi, Laura 3 Madden, James J. 3 Mezey, Paul G. 3 Milman, Pierre D. 3 Neumann, Walter David 3 Parusiński, Adam 3 Popescu-Pampu, Patrick 3 Reguera, Ana-José 3 Snoussi, Jawad 3 Taylor, Keith Frederick 3 Temkin, Michael 3 Tornero, José María 3 Veys, Willem 3 Vos, Lena 2 Akéké, Eric Dago 2 Beck, Tobias 2 Beddani, Charef 2 Bondil, Romain 2 Datta, Rankeya 2 de Moraes, Michael 2 Faber, Eleonore 2 Fernández de Bobadilla, Javier 2 Fernandez, Julio 2 Giles Flores, Arturo 2 Fortuny Ayuso, Pedro 2 García Barroso, Evelia Rosa 2 González Pérez, Pedro Daniel 2 Guàrdia, Jordi 2 Gusein-Zade, Sabir M. 2 Heinzer, William J. 2 Hyry, Eero 2 Järvilehto, Tarmo 2 Källström, Rolf 2 Khan, Adeel A. 2 Kiyek, Karl-Heinz 2 Kollár, János 2 Kovács, Sándor J. 2 Leyton-Alvarez, Maximiliano 2 Lieblich, Max David 2 Mahboub, Wael 2 Martín-Morales, Jorge 2 Moreno-Ávila, Carlos-Jesús 2 Némethi, András 2 Novacoski, J. A. 2 Olberding, Bruce M. 2 Pe Pereira, María 2 Piedra, Ramon 2 Plénat, Camille 2 Reis, Helena 2 Ribón, Javier 2 Roche, Claude Andre 2 San Saturnino, Jean-Christophe 2 Sanz Sánchez, Fernando 2 Silva de Souza, C. H. 2 Yoshida, Eiji 1 Abramovich, Dan 1 Adamus, Janusz 1 Alonso, Mariemi E. ...and 134 more Authors all top 5 Cited in 76 Serials 35 Journal of Algebra 25 Journal of Pure and Applied Algebra 15 Communications in Algebra 10 Advances in Mathematics 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 10 Journal of Mathematical Chemistry 9 Transactions of the American Mathematical Society 8 Annales de l’Institut Fourier 7 Manuscripta Mathematica 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 5 Journal of the London Mathematical Society. Second Series 5 Mathematische Zeitschrift 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Algebra & Number Theory 4 Mathematische Annalen 4 Bulletin of the American Mathematical Society. New Series 4 Journal of Algebra and its Applications 4 Journal of Singularities 3 Compositio Mathematica 3 Michigan Mathematical Journal 3 Revista Matemática Iberoamericana 3 International Journal of Mathematics 3 Revista Matemática Complutense 3 Annals of Mathematics. Second Series 3 Journal of Commutative Algebra 2 Bulletin de la Société Mathématique de France 2 Duke Mathematical Journal 2 Inventiones Mathematicae 2 Memoirs of the American Mathematical Society 2 Pacific Journal of Mathematics 2 Proceedings of the American Mathematical Society 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Rendiconti del Seminario Matematico della Università di Padova 2 Results in Mathematics 2 Journal of Symbolic Computation 2 Journal of the American Mathematical Society 2 Designs, Codes and Cryptography 2 Journal of Algebraic Geometry 2 Finite Fields and their Applications 1 American Mathematical Monthly 1 Israel Journal of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Acta Mathematica 1 Acta Mathematica Vietnamica 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Canadian Journal of Mathematics 1 Illinois Journal of Mathematics 1 Publications Mathématiques 1 Monatshefte für Mathematik 1 Osaka Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 Topology and its Applications 1 European Journal of Combinatorics 1 Publicacions Matemàtiques 1 International Journal of Algebra and Computation 1 IMRN. International Mathematics Research Notices 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Indagationes Mathematicae. New Series 1 Applicable Algebra in Engineering, Communication and Computing 1 Experimental Mathematics 1 Algebra Colloquium 1 Bulletin des Sciences Mathématiques 1 The Ramanujan Journal 1 Geometry & Topology 1 Algebras and Representation Theory 1 Qualitative Theory of Dynamical Systems 1 Advances in Geometry 1 Foundations of Computational Mathematics 1 International Journal of Number Theory 1 Journal of Physics A: Mathematical and Theoretical 1 Japanese Journal of Mathematics. 3rd Series 1 Kyoto Journal of Mathematics 1 Journal de l’École Polytechnique – Mathématiques all top 5 Cited in 29 Fields 176 Algebraic geometry (14-XX) 137 Commutative algebra (13-XX) 72 Several complex variables and analytic spaces (32-XX) 31 Field theory and polynomials (12-XX) 15 Number theory (11-XX) 13 Associative rings and algebras (16-XX) 10 Biology and other natural sciences (92-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 History and biography (01-XX) 5 Functional analysis (46-XX) 5 Convex and discrete geometry (52-XX) 5 Information and communication theory, circuits (94-XX) 4 Mathematical logic and foundations (03-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Combinatorics (05-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Group theory and generalizations (20-XX) 3 Manifolds and cell complexes (57-XX) 3 Quantum theory (81-XX) 2 \(K\)-theory (19-XX) 1 General algebraic systems (08-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.