English

# Item

ITEM ACTIONSEXPORT
Motivic classes of moduli of Higgs bundles and moduli of bundles with connections

Fedorov, R., Soibelman, A., & Soibelman, Y. (2018). Motivic classes of moduli of Higgs bundles and moduli of bundles with connections. Communications in Number Theory and Physics, 12(4), 687-766. doi:10.4310/CNTP.2018.v12.n4.a3.

Item is

### Basic

show hide
Genre: Journal Article

### Files

show Files
hide Files
:
arXiv:1705.04890.pdf (Preprint), 642KB
Name:
arXiv:1705.04890.pdf
Description:
OA-Status:
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
-
-
:
Fedorov_Motivic classes of moduli of Higgs bundles_2018.pdf (Publisher version), 611KB

-
Name:
Fedorov_Motivic classes of moduli of Higgs bundles_2018.pdf
Description:
-
OA-Status:
Visibility:
Restricted (Max Planck Institute for Mathematics, MBMT; )
MIME-Type / Checksum:
application/pdf
-
-
-

### Locators

show
hide
Locator:
http://dx.doi.org/10.4310/CNTP.2018.v12.n4.a3 (Publisher version)
Description:
-
OA-Status:

### Creators

show
hide
Creators:
Fedorov, Roman1, Author
Soibelman, Alexander, Author
Soibelman, Yan, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201

### Content

show
hide
Free keywords: Mathematics, Algebraic Geometry, High Energy Physics - Theory, Complex Variables, Quantum Algebra, Symplectic Geometry
Abstract: Let X be a smooth projective curve over a field of characteristic zero. We calculate the motivic class of the moduli stack of semistable Higgs bundles on X. We also calculate the motivic class of the moduli stack of vector bundles with connections by showing that it is equal to the class of the stack of semistable Higgs bundles of the same rank and degree zero. We follow the strategy of Mozgovoy and Schiffmann for counting Higgs bundles over finite fields. The main new ingredient is a motivic version of a theorem of Harder about Eisenstein series claiming that all vector bundles have
approximately the same motivic class of Borel reductions as the degree of Borel
reduction tends to $-\infty$.

### Details

show
hide
Language(s): eng - English
Dates: 2018
Publication Status: Published in print
Pages: -
Publishing info: -
Rev. Type: Peer
Identifiers:
Degree: -

show

show

show

### Source 1

show
hide
Title: Communications in Number Theory and Physics
Abbreviation : Commun. Number Theory Phys.
Source Genre: Journal
Creator(s):
Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 12 (4) Sequence Number: - Start / End Page: 687 - 766 Identifier: -