國立虎尾科技大學 |

Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification./
Author:	Schieder, Simon Fabian.
Description:	1 online resource (116 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
Contained By:	Dissertation Abstracts International77-04B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781339296210

Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification.
Schieder, Simon Fabian.

Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification. - 1 online resource (116 pages)

Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.

Thesis (Ph.D.)--Harvard University, 2015.

Includes bibliographical references

We study the singularities of the Drinfeld-Lafforgue-Vinberg compactification of the moduli stack of G-bundles on a smooth projective curve for a reductive group G. The study of these compactifications was initiated by V. Drinfeld (for G=GL2) and continued by L. Lafforgue (for G=GLn) in their work on the Langlands correspondence for function fields; unlike the work of Drinfeld and Lafforgue, however, we focus on questions about the singularities of these compactifications which arise naturally in the geometric Langlands program. A definition of the compactification for a general reductive group G is also due to Drinfeld (unpublished) and relies on the Vinberg semigroup of G; this case will be dealt with in the forthcoming work [Sch]. In the present work we focus on the case G=SL 2. In this case the compactification can alternatively be viewed as a canonical one-parameter degeneration of the moduli space of SL2-bundles. We study the singularities of this one-parameter degeneration via the weight-monodromy theory of the associated nearby cycles construction: We give an explicit description of the nearby cycles sheaf together with its monodromy action in terms of certain novel perverse sheaves which we call "Picard-Lefschetz oscillators", and then use this description to determine the intersection cohomology sheaf and other invariants of the singularities. Our proofs rely on the construction of certain local models for the one-parameter degeneration which themselves form one-parameter families of spaces which are factorizable in the sense of Beilinson and Drinfeld. We also include a first application on the level of functions.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781339296210Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification.
LDR:02873ntm a2200325Ki 4500 001 918755
005 20181030085013.5
006 m o u
007 cr mn||||a|a||
008 190606s2015 xx obm 000 0 eng d
020 $a 9781339296210
035 $a (MiAaPQ)AAI3739083
035 $a (MiAaPQ)vireo:harvard266Schieder
035 $a AAI3739083
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Schieder, Simon Fabian. $3 1193165
245 1 0 $a Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification.
264 0 $c 2015
300 $a 1 online resource (116 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
500 $a Adviser: Dennis Gaitsgory.
502 $a Thesis (Ph.D.)--Harvard University, 2015.
504 $a Includes bibliographical references
520 $a We study the singularities of the Drinfeld-Lafforgue-Vinberg compactification of the moduli stack of G-bundles on a smooth projective curve for a reductive group G. The study of these compactifications was initiated by V. Drinfeld (for G=GL2) and continued by L. Lafforgue (for G=GLn) in their work on the Langlands correspondence for function fields; unlike the work of Drinfeld and Lafforgue, however, we focus on questions about the singularities of these compactifications which arise naturally in the geometric Langlands program. A definition of the compactification for a general reductive group G is also due to Drinfeld (unpublished) and relies on the Vinberg semigroup of G; this case will be dealt with in the forthcoming work [Sch]. In the present work we focus on the case G=SL 2. In this case the compactification can alternatively be viewed as a canonical one-parameter degeneration of the moduli space of SL2-bundles. We study the singularities of this one-parameter degeneration via the weight-monodromy theory of the associated nearby cycles construction: We give an explicit description of the nearby cycles sheaf together with its monodromy action in terms of certain novel perverse sheaves which we call "Picard-Lefschetz oscillators", and then use this description to determine the intersection cohomology sheaf and other invariants of the singularities. Our proofs rely on the construction of certain local models for the one-parameter degeneration which themselves form one-parameter families of spaces which are factorizable in the sense of Beilinson and Drinfeld. We also include a first application on the level of functions.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Harvard University. $b Mathematics. $3 1193029
773 0 $t Dissertation Abstracts International $g 77-04B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3739083 $z click for full text (PQDT)