Vladimir Aleksandrovich Voevodsky (obituary)

A. A. Beilinson ; A. S. Vishik ; D. A. Kazhdan ; M. M. Kapranov ; A. S. Merkurjev ; D. O. Orlov ; I. A. Panin ; A. A. Suslin ; N. A. Tyurin ; G. B. Shabat

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 73 (2018) no. 3, pp. 519-531

Bibliographie

[1] “Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields”, Soviet Math. Dokl., 39:1 (1989), 38–41 (with G. B. Shabat) | MR | Zbl

[2] “Drawing curves over number fields”, The Grothendieck Festschrift, v. III, Progr. Math., 88, Birkhäuser Boston, Boston, MA, 1990, 199–227 (with G. B. Shabat) | DOI | MR | Zbl

[3] “Étale topologies of schemes over fields of finite type over $\mathbf Q$”, Math. USSR-Izv., 37:3 (1991), 511–523 | DOI | MR | Zbl

[4] “$\infty$-groupoids as a model for a homotopy category”, Russian Math. Surveys, 45:5 (1990), 239–240 (with M. M. Kapranov) | DOI | MR | Zbl

[5] “Free $n$-category generated by a cube, oriented matroids, and higher Bruhat orders”, Funct. Anal. Appl., 25:1 (1991), 50–52 (with M. M. Kapranov) | DOI | MR | Zbl

[6] “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., 32:1 (1991), 11–27 (with M. M. Kapranov) | MR | Zbl

[7] “$\infty$-groupoids and homotopy types”, International category theory meeting (Bangor, 1989 and Cambridge, 1990), Cahiers Topologie Géom. Différentielle Catég., 32:1 (1991), 29–46 (with M. M. Kapranov) | MR | Zbl

[8] “On Galois groups of function fields over fields of finite type over $\mathbb Q$”, Russian Math. Surveys, 46:5 (1991), 202–203 | DOI | MR | Zbl

[9] “Galois representations connected with hyperbolic curves”, Math. USSR-Izv., 39:3 (1992), 1281–1291 | DOI | MR | Zbl

[10] “$2$-categories and Zamolodchikov tetrahedra equations”, Algebraic groups and their generalizations: quantum infinite-dimensional methods (University Park, PA, 1991), Proc. Sympos. Pure Math., 56, Part 2, Amer. Math. Soc., Providence, RI, 1994, 177–259 (with M. M. Kapranov) | DOI | MR | Zbl

[11] “Braided monoidal $2$-categories and Manin–Schechtman higher braid groups”, J. Pure Appl. Algebra, 92:3 (1994), 241–267 (with M. Kapranov) | DOI | MR | Zbl

[12] Homology of schemes and covariant motives, Ph.D. Thesis, Harvard Univ., Cambridge, MA, 1992, 64 pp. | MR

[13] “A nilpotence theorem for cycles algebraically equivalent to zero”, Int. Math. Res. Not., 1995, no. 4, 187–198 | DOI | MR | Zbl

[14] “Homology of schemes”, Selecta Math. (N. S.), 2:1 (1996), 111–153 | DOI | MR | Zbl

[15] “Singular homology of abstract algebraic varieties”, Invent. Math., 123:1 (1996), 61–94 (with A. Suslin) | DOI | MR | Zbl

[16] “$\mathbf A^1$-homotopy theory”, Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), Doc. Math., 1998, Extra Vol. I, 579–604 | MR | Zbl

[17] “${\mathbf A}^1$-homotopy theory of schemes”, Inst. Hautes Études Sci. Publ. Math., 1999, no. 90, 45–143 (with F. Morel) | DOI | MR | Zbl

[18] “Voevodsky's Seattle lectures: $K$-theory and motivic cohomology”, Notes by C. Weibel, Algebraic $K$-theory (Seattle, WA, 1997), Proc. Sympos. Pure Math., 67, Amer. Math. Soc., Providence, RI, 1999, 283–303 | DOI | MR | Zbl

[19] “Introduction”, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 3–9 (with E. M. Friedlander, A. Suslin) | MR | Zbl

[20] “Relative cycles and Chow sheaves”, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 10–86 (with A. Suslin) | MR | Zbl

[21] “Cohomological theory of presheaves with transfers”, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 87–137 | MR | Zbl

[22] “Bivariant cycle cohomology”, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 138–187 (with E. M. Friedlander) | MR | Zbl

[23] “Triangulated categories of motives over a field”, Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000, 188–238 | MR | Zbl

[24] Cycles, transfers, and motivic homology theories, Ann. of Math. Stud., 143, Princeton Univ. Press, Princeton, NJ, 2000 (with E. M. Friedlander, A. Suslin), vi+254 pp. | MR | Zbl

[25] “Bloch–Kato conjecture and motivic cohomology with finite coefficients”, The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), NATO Sci. Ser. C Math. Phys. Sci., 548, Kluwer Acad. Publ., Dordrecht, 2000, 117–189 (with A. Suslin) | DOI | MR | Zbl

[26] “Open problems in the motivic stable homotopy theory. I”, Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), Int. Press Lect. Ser., 3, 1, Int. Press, Somerville, MA, 2002, 3–34 | MR | Zbl

[27] “A possible new approach to the motivic spectral sequence for algebraic $K$-theory”, Recent progress in homotopy theory (Baltimore, MD, 2000), Contemp. Math., 293, Amer. Math. Soc., Providence, RI, 2002, 371–379 | DOI | MR | Zbl

[28] “Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic”, Int. Math. Res. Not., 2002, no. 7, 351–355 | DOI | MR | Zbl

[29] “Reduced power operations in motivic cohomology”, Publ. Math. Inst. Hautes Études Sci., 2003, no. 98, 1–57 | DOI | MR | Zbl

[30] “Motivic cohomology with ${\mathbb Z}/2$-coefficients”, Publ. Math. Inst. Hautes Études Sci., 2003, no. 98, 59–104 | DOI | MR | Zbl

[31] “On the zero slice of the sphere spectrum”, Algebraicheskaya geometriya: Metody, svyazi i prilozheniya, Sbornik statei. Posvyaschaetsya pamyati chlena-korrespondenta RAN Andreya Nikolaevicha Tyurina, Tr. MIAN, 246, Nauka, MAIK “Nauka/Interperiodika”, M., 2004, 106–115 | MR | Zbl

[32] Lecture notes on motivic cohomology, Clay Math. Monogr., 2, Amer. Math. Soc., Providence, RI; Clay Math. Inst., Cambridge, MA, 2006 (with C. Mazza, Ch. Weibel), xiv+216 pp. | MR | Zbl

[33] “An exact sequence for $K^M_\ast/2$ with applications to quadratic forms”, Ann. of Math. (2), 165:1 (2007), 1–13 (with D. Orlov, A. Vishik) | DOI | MR | Zbl

[34] “Voevodsky's Nordfjordeid lectures: motivic homotopy theory”, Motivic homotopy theory, Universitext, Springer, Berlin, 2007, 147–221 (with O. Röndigs, P. A. Østvær) | DOI | MR

[35] Motivic homotopy theory, Lectures from the summer school (Nordfjordeid, 2002), Universitext, Springer-Verlag, Berlin, 2007 (with B. I. Dundas, M. Levine, P. A. Østvær, O. Röndigs), x+221 pp. | DOI | MR | Zbl

[36] “Cancellation theorem”, Doc. Math., 2010, Extra vol.: A. A. Suslin sixtieth birthday, 671–685 | MR | Zbl

[37] “Motives over simplicial schemes”, J. K-Theory, 5:1 (2010), 1–38 | DOI | MR | Zbl

[38] “Simplicial radditive functors”, J. K-Theory, 5:2 (2010), 201–244 | DOI | MR | Zbl

[39] “Motivic Eilenberg–MacLane spaces”, Publ. Math. Inst. Hautes Études Sci., 2010, no. 112, 1–99 | DOI | MR | Zbl

[40] “Homotopy theory of simplicial sheaves in completely decomposable topologies”, J. Pure Appl. Algebra, 214:8 (2010), 1384–1398 | DOI | MR | Zbl

[41] “Unstable motivic homotopy categories in Nisnevich and cdh-topologies”, J. Pure Appl. Algebra, 214:8 (2010), 1399–1406 | DOI | MR | Zbl

[42] “On motivic cohomology with $\mathbb Z/l$-coefficients”, Ann. of Math. (2), 174:1 (2011), 401–438 | DOI | MR | Zbl

[43] Abstracts from the mini-workshop (February 27 – March 05, 2011), Oberwolfach Rep., 8, no. 1, 2011 (ed. by V. Voevodsky with S. Awodey, R. Garner, P. Martin-Löf) | DOI | MR | Zbl

[44] “Univalent foundations of mathematics”, Logic, language, information and computation (Philadelphia, PA, 2011), Lecture Notes in Comput. Sci., 6642, Lecture Notes in Artificial Intelligence, Springer, Heidelberg, 2011, 4 | DOI | MR | Zbl

[45] “A univalent formalization of the $p$-adic numbers”, Math. Structures Comput. Sci., 25:5 (2015), 1147–1171 (with Á. Pelayo, M. A. Warren) | DOI | MR | Zbl

[46] “An experimental library of formalized mathematics based on the univalent foundations”, Math. Structures Comput. Sci., 25:5 (2015), 1278–1294 | DOI | MR | Zbl

[47] “A C-system defined by a universe category”, Theory Appl. Categ., 30 (2015), No 37, 1181–1215 | MR | Zbl

[48] “Subsystems and regular quotients of C-systems”, A panorama of mathematics: pure and applied, Contemp. Math., 658, Amer. Math. Soc., Providence, RI, 2016, 127–137 | DOI | MR | Zbl

[49] “Products of families of types and $(\Pi,\lambda)$-structures on C-systems”, Theory Appl. Categ., 31 (2016), No 36, 1044–1094 | MR | Zbl

[50] “C-systems defined by universe categories: presheaves”, Theory Appl. Categ., 32 (2017), No 3, 53–112 | MR | Zbl

[51] “The $(\Pi, \lambda)$-structures on the C-systems defined by universe categories”, Theory Appl. Categ., 32 (2017), No 4, 113–121 | MR | Zbl

[52] “Categorical structures for type theory in univalent foundations”, Computer science logic 2017, LIPIcs. Leibniz Int. Proc. Inform., 82, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2017, 8 (with B. Ahrens, P. L. Lumsdaine), 16 pp. | DOI | MR