Publications

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2017
Voevodsky, V., "The C-systems defined by universe categories: presheaves", Theory and Applications of Categories, vol. 32, issue 3, pp. 53-112, 01/2017.  (618.12 KB)
Voevodsky, V., "The $(\Pi,\lambda)$-structures on the C-systems defined by universe categories", Theory and Applications of Categories, vol. 32, issue 4, pp. 113-121, 01/2017.  (296.95 KB)
2016
Voevodsky, V., "Lawvere theories and Jf-relative monads", arXiv 1601.02158, pp. 1--21, 2016.
Voevodsky, V., "Products of families of types and $(\Pi,\lambda)$-structures on C-systems", Theory Appl. Categ., vol. 31, pp. No. 36, 1044-1094, 11/2016.  (565.01 KB)
2015
Voevodsky, V., "A C-system defined by a universe category", Theory Appl. Categ., vol. 30, pp. No. 37, 1181–1215, 2015.
Prepublication versions in arXiv.
 (449.89 KB)
Voevodsky, V., "An experimental library of formalized Mathematics based on the univalent foundations", Mathematical Structures in Computer Science, vol. FirstView, pp. 1–17, 2, 2015.
Pre-publication version is here.
Voevodsky, V., "Lawvere theories and C-systems", arXiv:1512.08104, pp. 15pp, 12/2015.  (250.57 KB)
Voevodsky, V., "Martin-Lof identity types in the C-systems defined by a universe category", arXiv 1505.06446, submitted, pp. 1–51, 2015.
Voevodsky, V., "Products of families of types in the C-systems defined by a universe category", arXiv 1503.07072, submitted, pp. 1–30, 2015.
Pelayo, Á., V. Voevodsky, and M. A. Warren, "A univalent formalization of the p-adic numbers", Mathematical Structures in Computer Science, vol. FirstView, pp. 1–25, 2, 2015.
The arXiv version is here.
2014
Voevodsky, V., "B-systems", arXiv 1410.5389, submitted, pp. 1–17, 2014.
Voevodsky, V., "C-system of a module over a monad on sets", arXiv 1407.3394, submitted, pp. 1–20, 2014.
Voevodsky, V., "Subsystems and regular quotients of C-systems", arXiv 1406.5389, submitted, pp. 1–11, 2014.
2011
Voevodsky, V., "On motivic cohomology with Z/l-coefficients", Ann. of Math. (2), vol. 174, pp. 401–438, 2011.  (505.13 KB)
2010
Voevodsky, V., "Cancellation theorem", Doc. Math., pp. 671–685, 2010.  (155.85 KB)
Voevodsky, V., "Homotopy theory of simplicial sheaves in completely decomposable topologies", J. Pure Appl. Algebra, vol. 214, pp. 1384–1398, 2010.  (762.49 KB)
Voevodsky, V., "Motives over simplicial schemes", J. K-Theory, vol. 5, pp. 1–38, 2010.  (325.11 KB)
Voevodsky, V., "Motivic Eilenberg-Maclane spaces", Publ. Math. Inst. Hautes Études Sci., pp. 1–99, 2010.  (915.29 KB)
Voevodsky, V., "Simplicial radditive functors", J. K-Theory, vol. 5, pp. 201–244, 2010.  (389.16 KB)
Voevodsky, V., "Univalent Foundations Project", a modified version of an NSF grant application, pp. 1–12, October, 2010.
Voevodsky, V., "Unstable motivic homotopy categories in Nisnevich and cdh-topologies", J. Pure Appl. Algebra, vol. 214, pp. 1399–1406, 2010.  (506.91 KB)
2007
Voevodsky, V., O. Röndigs, and P. Arne Ø. stvær, "Voevodsky's Nordfjordeid lectures: motivic homotopy theory", Motivic homotopy theory: Springer, Berlin, pp. 147–221, 2007.  (1.12 MB)
2006
Mazza, C., V. Voevodsky, and C. Weibel, "Lecture notes on motivic cohomology", Clay Mathematics Monographs, vol. 2: American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, pp. xiv+216, 2006.  (1.34 MB)
Voevodsky, V., "A very short note on homotopy $\lambda$-calculus", Unpublished, pp. 1–7, September, 2006.  (113.85 KB)
2003
Voevodsky, V., "Motivic cohomology with Z/2-coefficients", Publ. Math. Inst. Hautes Études Sci., pp. 59–104, 2003.
There were several papers that preceded this paper that explored other proofs of the Milnor Conjecture based on the same general direction of approach. Ultimately it was the present paper that was published in a journal since the proof that it contained was most direct and required the least amount of preliminary work. The earlier versions of the proof are available here: Bloch-Kato conjecture for Z/2-coefficients and algebraic Morava K-theories (June 1995).  The Milnor Conjecture (December 1996) On 2-torsion in motivic cohomology (July 2001) Motivic cohomology with Z/2-coefficients (published version, 2003).  
Voevodsky, V., "Reduced power operations in motivic cohomology", Publ. Math. Inst. Hautes Études Sci., pp. 1–57, 2003.  (542.94 KB)
2002
Voevodsky, V., "Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic", Int. Math. Res. Not., pp. 351–355, 2002.  (87.25 KB)
Voevodsky, V., "Open problems in the motivic stable homotopy theory. I", Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), vol. 3: Int. Press, Somerville, MA, pp. 3–34, 2002.  (3.04 MB)
Voevodsky, V., "A possible new approach to the motivic spectral sequence for algebraic K-theory", Recent progress in homotopy theory Baltimore, MD, 2000), vol. 293: Amer. Math. Soc., Providence, RI, pp. 371–379, 2002.  (810.81 KB)
2000
Friedlander, E. M., and V. Voevodsky, "Bivariant cycle cohomology", Cycles, transfers, and motivic homology theories, vol. 143: Princeton Univ. Press, Princeton, NJ, pp. 138–187, 2000.  (348.23 KB)
Suslin, A., and V. Voevodsky, "Bloch-Kato conjecture and motivic cohomology with finite coefficients", The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), vol. 548: Kluwer Acad. Publ., Dordrecht, pp. 117–189, 2000.  (618.57 KB)
Voevodsky, V., "Cohomological theory of presheaves with transfers", Cycles, transfers, and motivic homology theories, vol. 143: Princeton Univ. Press, Princeton, NJ, pp. 87–137, 2000.  (346.26 KB)
Suslin, A., and V. Voevodsky, "Relative cycles and Chow sheaves", Cycles, transfers, and motivic homology theories, vol. 143: Princeton Univ. Press, Princeton, NJ, pp. 10–86, 2000.  (524.85 KB)
Voevodsky, V., "Triangulated categories of motives over a field", Cycles, transfers, and motivic homology theories, vol. 143: Princeton Univ. Press, Princeton, NJ, pp. 188–238, 2000.  (346.26 KB)
1999
Morel, F., and V. Voevodsky, "A^1-homotopy theory of schemes", Inst. Hautes Études Sci. Publ. Math., pp. 45–143 (2001), 1999.  (9.25 MB)
Voevodsky, V., "Categories and functors in mathematics", Unpublished, pp. 1–18, 1999.
Voevodsky, V., "Four functors formalism", Unpublished, pp. 1–20, March, 1999.
One of the most important ideas of the four functor formalism was the proof that a projective morphism is lower transversal (satisfies a generalized analog of the proper base change theorem). Unfortunately no complete proof remained but all of the main ideas are contained in these notes: 1998-11-13-notes.pdf 1998-11-21-notes.pdf 2002-01-08-notes.pdf
 (77.92 KB)
1998
Voevodsky, V., "A^1-homotopy theory", Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), 1998.  (355.89 KB)
1996
Suslin, A., and V. Voevodsky, "Singular homology of abstract algebraic varieties", Invent. Math., vol. 123, pp. 61–94, 1996.  (1.56 MB)
1992
Voevodsky, V., Homology of schemes and covariant motives, : ProQuest LLC, Ann Arbor, MI, pp. 64, 1992.
Thesis (Ph.D.)–Harvard University
 (3.48 MB)