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The Atiyah-Bott theorem for algebrai...

Kotov, Vladimir.

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The Atiyah-Bott theorem for algebraic surfaces.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The Atiyah-Bott theorem for algebraic surfaces./
Author:	Kotov, Vladimir.
Description:	44 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
Contained By:	Dissertation Abstracts International74-07B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3556623
ISBN:	9781267988638

The Atiyah-Bott theorem for algebraic surfaces.
Kotov, Vladimir.

The Atiyah-Bott theorem for algebraic surfaces. - 44 p.

Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.

Thesis (Ph.D.)--Northwestern University, 2013.

Following D. Gaitsgory, we give a conceptual proof of a classical result of Atiyah and Bott about the cohomology ring of a moduli space Bun G of G-principal bundles on an algebraic curve. We write down its cohomology as a chiral homology of a certain very natural chiral algebra on the curve. And then we compute this chiral homology using various methods developed by Gaitsgory, Beilinson and Drinfeld.

ISBN: 9781267988638Subjects--Topical Terms:

515831
Mathematics.

The Atiyah-Bott theorem for algebraic surfaces.
LDR:01725nam a2200289 4500 001 1964688
005 20141010092803.5
008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781267988638
035 $a (MiAaPQ)AAI3556623
035 $a AAI3556623
040 $a MiAaPQ $c MiAaPQ
100 1 $a Kotov, Vladimir. $3 2101185
245 1 4 $a The Atiyah-Bott theorem for algebraic surfaces.
300 $a 44 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
500 $a Adviser: Kevin Costello.
502 $a Thesis (Ph.D.)--Northwestern University, 2013.
520 $a Following D. Gaitsgory, we give a conceptual proof of a classical result of Atiyah and Bott about the cohomology ring of a moduli space Bun G of G-principal bundles on an algebraic curve. We write down its cohomology as a chiral homology of a certain very natural chiral algebra on the curve. And then we compute this chiral homology using various methods developed by Gaitsgory, Beilinson and Drinfeld.
520 $a We give an analog of this result for the two-dimensional case, where we use a Hilbert scheme of a surface in place of BunG. That is, we compute the cohomology of the Hilbert scheme in a very similar manner as we did for curves. We notice that the Hilbert scheme factorizes similarly to Beilinson-Drinfeld Grassmanian. Using this factorization structure, we find a chiral algebra on our surface, whose chiral homology is the cohomology ring of the Hilbert scheme.
590 $a School code: 0163.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a Northwestern University. $b Mathematics. $3 1280008
773 0 $t Dissertation Abstracts International $g 74-07B(E).
790 $a 0163
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3556623