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D
Deligne, P., "Voevodsky's lectures on motivic cohomology 2000/2001", Algebraic topology, vol. 4: Springer, Berlin, pp. 355–409, 2009. [PDF] (735.89 KB)
Deligne, P., "Voevodsky's lectures on cross functors, Fall 2001", Unpublished, pp. 1–41, 2001. [PDF] (369.71 KB)
F
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. [PDF] (348.23 KB)
Friedlander, E. M., A.. Suslin, and V.. Voevodsky, "Introduction", Cycles, transfers, and motivic homology theories, vol. 143: Princeton Univ. Press, Princeton, NJ, pp. 3–9, 2000. [PDF] (76.77 KB)
K
Kapranov, M.., and V.. Voevodsky, "Braided monoidal 2-categories and Manin-Schechtman higher braid groups", J. Pure Appl. Algebra, vol. 92, pp. 241–267, 1994. [PDF] (1.51 MB)
Kapranov, M.. M., and V.. A. Voevodsky, "Combinatorial-geometric aspects of polycategory theory: pasting schemes and higher Bruhat orders (list of results)", Cahiers Topologie Géom. Différentielle Catég., vol. 32, pp. 11–27, 1991.
International Category Theory Meeting (Bangor, 1989 and Cambridge, 1990)
[PDF] (1.28 MB)
Kapranov, M.. M., and V.. A. Voevodsky, "2-categories and Zamolodchikov tetrahedra equations", Algebraic groups and their generalizations: quantum and infinite-dimensional methods (University Park, PA, 1991), vol. 56: Amer. Math. Soc., Providence, RI, pp. 177–259, 1994. [PDF] (7.42 MB)
Kapranov, M.. M., and V.. A. Voevodsky, "infty-groupoids and homotopy types", Cahiers Topologie Géom. Différentielle Catég., vol. 32, pp. 29–46, 1991.
International Category Theory Meeting (Bangor, 1989 and Cambridge, 1990)

Warning: the main theorem of this paper was shown by Carlos Simpson to be false.   
[PDF] (1.34 MB)
M
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. [PDF] (1.34 MB)
Morel, F., and V. Voevodsky, "A^1-homotopy theory of schemes", Inst. Hautes Études Sci. Publ. Math., pp. 45–143 (2001), 1999. [PDF] (9.25 MB)
O
Orlov, D.., A.. Vishik, and V.. Voevodsky, "An exact sequence for K^M/2 with applications to quadratic forms", Ann. of Math. (2), vol. 165, pp. 1–13, 2007. [PDF] (336.38 KB)
P
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.
S
Shabat, G.. B., and V.. A. Voevodsky, "Drawing curves over number fields", The Grothendieck Festschrift, Vol. III, vol. 88: Birkhäuser Boston, Boston, MA, pp. 199–227, 1990. [PDF] (2.02 MB)
Suslin, A., and V. Voevodsky, "Singular homology of abstract algebraic varieties", Invent. Math., vol. 123, pp. 61–94, 1996. [PDF] (1.56 MB)
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. [PDF] (618.57 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. [PDF] (524.85 KB)
V
Voevodsky, V.., "A nilpotence theorem for cycles algebraically equivalent to zero", Internat. Math. Res. Notices, pp. 187–198 (electronic), 1995. [PDF] (98.87 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. [PDF] (296.95 KB)
Voevodsky, V., "On motivic cohomology with Z/l-coefficients", Ann. of Math. (2), vol. 174, pp. 401–438, 2011. [PDF] (505.13 KB)
Voevodsky, V., "Motives over simplicial schemes", J. K-Theory, vol. 5, pp. 1–38, 2010. [PDF] (325.11 KB)
Voevodsky, V.. A., "Etale topologies of schemes over fields of finite type over Q", Izv. Akad. Nauk SSSR Ser. Mat., vol. 54, pp. 1155–1167, 1990. [PDF] (713.56 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. [PDF] (3.04 MB)
Voevodsky, V., "The equivalence axiom and univalent models of type theory", arXiv 1402.5556, pp. 1–11, 2010.
Voevodsky, V., "Subsystems and regular quotients of C-systems", arXiv 1406.5389, submitted, pp. 1–11, 2014.
Voevodsky, V.. A., "Galois representations connected with hyperbolic curves", Izv. Akad. Nauk SSSR Ser. Mat., vol. 55, pp. 1331–1342, 1991. [PDF] (667.54 KB)
Voevodsky, V.. A., "Galois Group over Q and Teihmuller Modular Groups", Proc. Conf. Constr. Methods and Alg. Number Theory, Minsk, 1989.
Voevodsky, V., "A very short note on homotopy $\lambda$-calculus", Unpublished, pp. 1–7, September, 2006. [PDF] (113.85 KB)
Voevodsky, V., "The C-systems defined by universe categories: presheaves", Theory and Applications of Categories, vol. 32, issue 3, pp. 53-112, 01/2017. [PDF] (618.12 KB)
Voevodsky, V., "Simplicial radditive functors", J. K-Theory, vol. 5, pp. 201–244, 2010. [PDF] (389.16 KB)
Voevodsky, V., "Reduced power operations in motivic cohomology", Publ. Math. Inst. Hautes Études Sci., pp. 1–57, 2003. [PDF] (542.94 KB)
Voevodsky, V.. A., "Triangulations of Oriented Manifolds and Ramified Coverings of Sphere (in Russian)", Proc. Conf. of Young Scientists: Moscow Univ. Press, 1990.
Voevodsky, V., "Products of families of types in the C-systems defined by a universe category", arXiv 1503.07072, submitted, pp. 1–30, 2015.
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.. A., "Galois groups of function fields over fields of finite type over Q", Uspekhi Mat. Nauk, vol. 46, pp. 163–164, 1991. [PDF] (148.48 KB)
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. [PDF] (1.12 MB)
Voevodsky, V., Homology of schemes and covariant motives, : ProQuest LLC, Ann Arbor, MI, pp. 64, 1992.
Thesis (Ph.D.)–Harvard University
[PDF] (3.48 MB)
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. [PDF] (346.26 KB)
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
[PDF] (77.92 KB)
Voevodsky, V.., "Homology of schemes", Selecta Math. (N.S.), vol. 2, pp. 111–153, 1996. [PDF] (2.44 MB)
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. [PDF] (565.01 KB)
Voevodsky, V., "Motivic Eilenberg-Maclane spaces", Publ. Math. Inst. Hautes Études Sci., pp. 1–99, 2010. [PDF] (915.29 KB)
Voevodsky, V.. A., and M.. M. Kapranov, "The free n-category generated by a cube, oriented matroids and higher Bruhat orders", Funktsional. Anal. i Prilozhen., vol. 25, pp. 62–65, 1991. [PDF] (235.89 KB)
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:  
Voevodsky, V.. A., and M.. M. Kapranov, "Multidimensional Categories (in Russian)", Proc. Conf. of Young Scientists: Moscow Univ. Press, 1990.
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., "Homotopy theory of simplicial sheaves in completely decomposable topologies", J. Pure Appl. Algebra, vol. 214, pp. 1384–1398, 2010. [PDF] (762.49 KB)
Voevodsky, V.. A., and G.. B. Shabat, "Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields", Dokl. Akad. Nauk SSSR, vol. 304, pp. 265–268, 1989. [PDF] (439.49 KB)
Voevodsky, V., "Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic", Int. Math. Res. Not., pp. 351–355, 2002. [PDF] (87.25 KB)
Voevodsky, V., "A^1-homotopy theory", Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), 1998. [PDF] (355.89 KB)
Voevodsky, V., "Lawvere theories and Jf-relative monads", arXiv 1601.02158, pp. 1--21, 2016.
Voevodsky, V., "C-system of a module over a monad on sets", arXiv 1407.3394, submitted, pp. 1–20, 2014.
Voevodsky, V.., "On the zero slice of the sphere spectrum", Tr. Mat. Inst. Steklova, vol. 246, pp. 106–115, 2004. [PDF] (207.32 KB)
Voevodsky, V.. A., and G.. B. Shabat, "Piece-Wise Euclidean Approximation of Jacobians of Algebraic Curves", CSTARCI Math. Preprints, 1990. [PDF] (1.23 MB)
Voevodsky, V., "Framed Correspondences", Unpublished, 2001. [PDF] (116.24 KB)
Voevodsky, V., "Lawvere theories and C-systems", arXiv:1512.08104, pp. 15pp, 12/2015. [PDF] (250.57 KB)
Voevodsky, V., "Cancellation theorem", Doc. Math., pp. 671–685, 2010. [PDF] (155.85 KB)
Voevodsky, V., "Unstable motivic homotopy categories in Nisnevich and cdh-topologies", J. Pure Appl. Algebra, vol. 214, pp. 1399–1406, 2010. [PDF] (506.91 KB)
Voevodsky, V.. A., and M.. M. Kapranov, "infty-groupoids as a model for a homotopy category", Uspekhi Mat. Nauk, vol. 45, pp. 183–184, 1990.
Warning: the main theorem of this paper was shown by Carlos Simpson to be false.
[PDF] (202.35 KB)
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. [PDF] (810.81 KB)
Voevodsky, V., "Categories and functors in mathematics", Unpublished, pp. 1–18, 1999.
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.
[PDF] (449.89 KB)
Voevodsky, V., "B-systems", arXiv 1410.5389, submitted, pp. 1–17, 2014.
Voevodsky, V.. A., "Flags and Grothendieck Cartographical Group in Higher Dimensions", CSTARCI Math. Preprints, 1990. [PDF] (583.06 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. [PDF] (346.26 KB)
Voevodsky, V., "Univalent Foundations Project", a modified version of an NSF grant application, pp. 1–12, October, 2010.
W
Weibel, C., "Voevodsky's Seattle lectures: K-theory and motivic cohomology", Algebraic K-theory (Seattle, WA, 1997), vol. 67: Amer. Math. Soc., Providence, RI, pp. 283–303, 1999. [PDF] (2.35 MB)