Cohomology of moduli spaces via a result of Chenevier and Lannes

Jonas Bergström; Carel Faber

doi:10.46298/epiga.2023.10307

Cohomology of moduli spaces via a result of Chenevier and Lannes

Jonas Bergström
, Carel Faber

Stockholm University

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We use a classification result of Chenevier and Lannes for algebraic automorphic representations together with a conjectural correspondence with ℓ-adic absolute Galois representations to determine the Euler characteristics (with values in the Grothendieck group of such representations) of M_3,n and M_3,n for n ≤ 14 and of local systems V_λ on A₃ for |λ| ≤ 16.

Original language	English
Article number	20
Pages (from-to)	1-14
Number of pages	14
Journal	Epijournal de Geometrie Algebrique
Volume	7
DOIs	https://doi.org/10.46298/epiga.2023.10307
Publication status	Published - 3 Oct 2023

Bibliographical note

Publisher Copyright:
© by the author(s)

Funding

We thank Gaëtan Chenevier and the referee for their helpful comments.

Keywords

Automorphic representations
Euler characteristic
Galois representations
Hecke operators
Lefschetz trace formula
moduli of abelian varieties
moduli of curves
Siegel modular forms

Access to Document

10.46298/epiga.2023.10307Licence: CC BY-SA

2207.05130Final published version, 514 KBLicence: CC BY-SA

Cite this

@article{6ac77ab323484e0291f651028fc4fc4d,

title = "Cohomology of moduli spaces via a result of Chenevier and Lannes",

abstract = "We use a classification result of Chenevier and Lannes for algebraic automorphic representations together with a conjectural correspondence with ℓ-adic absolute Galois representations to determine the Euler characteristics (with values in the Grothendieck group of such representations) of M3,n and M3,n for n ≤ 14 and of local systems Vλ on A3 for |λ| ≤ 16.",

keywords = "Automorphic representations, Euler characteristic, Galois representations, Hecke operators, Lefschetz trace formula, moduli of abelian varieties, moduli of curves, Siegel modular forms",

author = "Jonas Bergstr{\"o}m and Carel Faber",

note = "Publisher Copyright: {\textcopyright} by the author(s)",

year = "2023",

month = oct,

day = "3",

doi = "10.46298/epiga.2023.10307",

language = "English",

volume = "7",

pages = "1--14",

journal = "Epijournal de Geometrie Algebrique",

issn = "2491-6765",

publisher = "Association de l'Epijournal de Geometrie Algebrique",

}

TY - JOUR

T1 - Cohomology of moduli spaces via a result of Chenevier and Lannes

AU - Bergström, Jonas

AU - Faber, Carel

N1 - Publisher Copyright: © by the author(s)

PY - 2023/10/3

Y1 - 2023/10/3

N2 - We use a classification result of Chenevier and Lannes for algebraic automorphic representations together with a conjectural correspondence with ℓ-adic absolute Galois representations to determine the Euler characteristics (with values in the Grothendieck group of such representations) of M3,n and M3,n for n ≤ 14 and of local systems Vλ on A3 for |λ| ≤ 16.

AB - We use a classification result of Chenevier and Lannes for algebraic automorphic representations together with a conjectural correspondence with ℓ-adic absolute Galois representations to determine the Euler characteristics (with values in the Grothendieck group of such representations) of M3,n and M3,n for n ≤ 14 and of local systems Vλ on A3 for |λ| ≤ 16.

KW - Automorphic representations

KW - Euler characteristic

KW - Galois representations

KW - Hecke operators

KW - Lefschetz trace formula

KW - moduli of abelian varieties

KW - moduli of curves

KW - Siegel modular forms

UR - https://www.scopus.com/pages/publications/85173829552

U2 - 10.46298/epiga.2023.10307

DO - 10.46298/epiga.2023.10307

M3 - Article

AN - SCOPUS:85173829552

SN - 2491-6765

VL - 7

SP - 1

EP - 14

JO - Epijournal de Geometrie Algebrique

JF - Epijournal de Geometrie Algebrique

M1 - 20

ER -

Cohomology of moduli spaces via a result of Chenevier and Lannes

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this