- Alexander Beilinson
Alexander A. Beilinson is the David and Mary Winton Green University Professor at the
University of Chicago and works on mathematics. His research has spannedrepresentation theory ,algebraic geometry andmathematical physics .Work
In 1981 Beilinson announced a proof of the
Kazhdan-Lusztig conjectures andJantzen conjectures withJoseph Bernstein . In 1982 Beilinson stated his own, seemingly profound conjectures about the existence ofmotivic cohomology groups for schemes, provided ashypercohomology group s of a complex ofabelian groups and related toalgebraic K-theory by amotivic spectral sequence , analogous to theAtiyah-Hirzebruch spectral sequence inalgebraic topology . These conjectures have since been dubbed theBeilinson-Soulé conjectures ; they are intertwined withVladimir Voevodsky 's program to develop ahomotopy theory forschemes .In 1984, Beilinson published a landmark paper entitled "Higher Regulators and values of L-functions" where he related
higher regulator s for K-theory and their relationship toL-functions . The paper also provided a generalization to arithmetic varieties of theLichtenbaum conjectures forK-group s of number rings, theHodge conjecture , theTate conjecture aboutalgebraic cycles , theBirch and Swinnerton-Dyer conjecture aboutelliptic curves , andBloch's conjecture about "K"2 of elliptic curves.Beilinson has also worked with
Drinfeld to totally rebuild the theory ofvertex algebra s. After many years of informal circulation, this research was finally published in 2004 in a form of a monograph onchiral algebra s. This has led to new advances inconformal field theory ,string theory and the geometricLanglands program .Selected publications
*cite book
author = Beilinson, A. A.; Drinfeld, V.
year = 2004
title = Chiral Algebras
publisher =American Mathematical Society
id = ISBN 978-0821835289*cite journal
author = Beilinson, A. A.
coauthors = Ginzburg, V. and Soergel, W.
title = Koszul duality patterns in representation theory
journal = Journal of the American Mathematical Society
volume = 9
year = 1996
issue = 2
pages = 473–527
id = ISSN: 0894-0347
doi = 10.1090/S0894-0347-96-00192-0*cite journal
author = Beilinson, A. A.
coauthors = Lusztig, G. and MacPherson, R.
title = A geometric setting for the quantum deformation of GLn
journal = Duke Mathematical Journal
volume = 61
year = 1990
issue = 2
pages = 655--677
id = ISSN: 0012-7094
doi = 10.1215/S0012-7094-90-06124-1*cite journal
author = Beilinson, A. A.
coauthors = Ginzburg, V. and Schechtman, V.
title = Koszul duality
journal = Journal of Geometry and Physics
volume = 5
year = 1988
issue = 3
pages = 317–350
id = ISSN: 0393-0440
doi = 10.1016/0393-0440(88)90028-9*cite conference
author = Beilinson, A. A.
title = How to glue perverse sheaves
booktitle = K-theory, arithmetic and geometry (Manin seminar, Moscow, 1984--1986) in Lecture Notes in Math.
publisher =Springer-Verlag
volume = 1289
pages = 42-51
year = 1987*cite conference
author = Beilinson, A. A.
title = On the derived category of perverse sheaves
booktitle = K-theory, arithmetic and geometry (Manin seminar, Moscow, 1984--1986) in Lecture Notes in Math.
publisher =Springer-Verlag
volume = 1289
pages = 27-41
year = 1987
*cite journal
author = Beilinson, A. A.
coauthors = MacPherson, R. and Schechtman, V.
title = Notes on motivic cohomology
journal = Duke Mathematical Journal
volume = 54
year = 1987
issue = 2
pages = 679--710
id = ISSN: 0012-7094
doi = 10.1215/S0012-7094-87-05430-5*cite conference
author = Beilinson, A. A.
title = Notes on absolute Hodge cohomology
booktitle = Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), Contemporary Mathematics
volume = 55
pages = 35-68
year = 1986
publisher = American Mathematical Society*cite conference
author = Beilinson, A. A.
title = Higher regulators and values of L-functions
publisher = Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow
booktitle = Itogi Nauki i Tekhniki, Current problems in mathematics
volume = 24
pages = 181-238
year = 1984*cite conference
author = Beilinson, A. A.
coauthors = Bernstein, J. and Deligne, P.
title = Faisceaux pervers
booktitle = Analysis and topology on singular spaces, I (Luminy, 1981), Astèrisque
volume = 100
pages = 5-171
publisher = Soc. Math. France, Paris
year = 1982*cite journal
author = Beilinson, A. A.
title = Residues and adèles
journal = Funktsional. Anal. i Prilozhen.
volume = 14
year = 1980
issue = 1
pages = 44–45
id = ISSN: 0374-1990*cite journal
author = Beilinson, A. A.
title = Coherent sheaves on "P"n and problems in linear algebra
journal = Funktsional. Anal. i Prilozhen.
volume = 12
year = 1978
issue = 3
pages = 68–69
id = ISSN: 0374-1990
doi = 10.1007/BF01681436References
*MathGenealogy|id=44354
External links
* [http://www.math.uiuc.edu/K-theory/0694/ Letter from Beilinson to Soule containing his conjectures on motivic cohomology]
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