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

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg compactification./
作者:	Schieder, Simon Fabian.
面頁冊數:	1 online resource (116 pages)
附註:	Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
Contained By:	Dissertation Abstracts International77-04B(E).
標題:	Mathematics. -
電子資源:	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 A definition of the compactification for a general reductive group G is also due to Drinfeld (unpublished) and relies on the Vinberg semigroup of G; this case will be dealt with in the forthcoming work [Sch].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.
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500 $a Source: Dissertation Abstracts International, Volume: 77-04(E), Section: B.
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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.
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538 $a Mode of access: World Wide Web
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