Alexander Beilinson

From Wikipedia, the free encyclopedia

This article needs additional citations for verification.
Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (December 2007)

Alexander A. Beilinson is the David and Mary Winton Green University Professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics.

1 Work
2 Selected publications
3 References
4 External links

[edit] Work

In 1981 Beilinson announced a proof of the Kazhdan-Lusztig conjectures and Jantzen conjectures with Joseph Bernstein. In 1982 Beilinson stated his own, seemingly profound conjectures about the existence of motivic cohomology groups for schemes, provided as hypercohomology groups of a complex of abelian groups and related to algebraic K-theory by a motivic spectral sequence, analogous to the Atiyah-Hirzebruch spectral sequence in algebraic topology. These conjectures have since been dubbed the Beilinson-Soulé conjectures; they are intertwined with Vladimir Voevodsky's program to develop a homotopy theory for schemes.

In 1984, Beilinson published a landmark paper entitled Higher Regulators and values of L-functions where he related higher regulators for K-theory and their relationship to L-functions. The paper also provided a generalization to arithmetic varieties of the Lichtenbaum conjectures for K-groups of number rings, the Hodge conjecture, the Tate conjecture about algebraic cycles, the Birch and Swinnerton-Dyer conjecture about elliptic curves, and Bloch's conjecture about K₂ of elliptic curves.

Beilinson has also worked with Drinfeld to totally rebuild the theory of vertex algebras. After many years of informal circulation, this research was finally published in 2004 in a form of a monograph on chiral algebras. This has led to new advances in conformal field theory, string theory and the geometric Langlands program.

[edit] Selected publications

Beilinson, A. A.; Drinfeld, V. (2004). Chiral Algebras. American Mathematical Society. ISBN 978-0821835289.

Beilinson, A. A.; Ginzburg, V. and Soergel, W. (1996). "Koszul duality patterns in representation theory". Journal of the American Mathematical Society 9 (2): 473–527. doi:10.1090/S0894-0347-96-00192-0. ISSN: 0894-0347.

Beilinson, A. A.; Lusztig, G. and MacPherson, R. (1990). "A geometric setting for the quantum deformation of GL_n". Duke Mathematical Journal 61 (2): 655--677. doi:10.1215/S0012-7094-90-06124-1. ISSN: 0012-7094.

Beilinson, A. A.; Ginzburg, V. and Schechtman, V. (1988). "Koszul duality". Journal of Geometry and Physics 5 (3): 317–350. doi:10.1016/0393-0440(88)90028-9. ISSN: 0393-0440.

Beilinson, A. A. (1987). "How to glue perverse sheaves". K-theory, arithmetic and geometry (Manin seminar, Moscow, 1984--1986) in Lecture Notes in Math. 1289: 42-51, Springer-Verlag.

Beilinson, A. A. (1987). "On the derived category of perverse sheaves". K-theory, arithmetic and geometry (Manin seminar, Moscow, 1984--1986) in Lecture Notes in Math. 1289: 27-41, Springer-Verlag.

Beilinson, A. A.; MacPherson, R. and Schechtman, V. (1987). "Notes on motivic cohomology". Duke Mathematical Journal 54 (2): 679--710. doi:10.1215/S0012-7094-87-05430-5. ISSN: 0012-7094.

Beilinson, A. A. (1986). "Notes on absolute Hodge cohomology". Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), Contemporary Mathematics 55: 35-68, American Mathematical Society.

Beilinson, A. A. (1984). "Higher regulators and values of L-functions". Itogi Nauki i Tekhniki, Current problems in mathematics 24: 181-238, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow.

Beilinson, A. A.; Bernstein, J. and Deligne, P. (1982). "Faisceaux pervers". Analysis and topology on singular spaces, I (Luminy, 1981), Astèrisque 100: 5-171, Soc. Math. France, Paris.

Beilinson, A. A. (1980). "Residues and adèles". Funktsional. Anal. i Prilozhen. 14 (1): 44–45. ISSN: 0374-1990.

Beilinson, A. A. (1978). "Coherent sheaves on Pⁿ and problems in linear algebra". Funktsional. Anal. i Prilozhen. 12 (3): 68–69. doi:10.1007/BF01681436. ISSN: 0374-1990.