Picard sheaves, local Brauer groups, and topological modular forms

Benjamin Antieau; Lennart Meier; Vesna Stojanoska

doi:10.48550/arXiv.2210.15743

Picard sheaves, local Brauer groups, and topological modular forms

Benjamin Antieau, Lennart Meier, Vesna Stojanoska

Research output: Working paper › Preprint › Academic

Abstract

We prove that the Brauer group of TMF is isomorphic to the Brauer group of the derived moduli stack of elliptic curves. Then, we compute the local Brauer group, i.e., the subgroup of the Brauer group of elements trivialized by some \'etale cover of the moduli stack, up to a finite 2-torsion group.

Original language	English
Publisher	arXiv
Pages	1-41
DOIs	https://doi.org/10.48550/arXiv.2210.15743
Publication status	Published - 27 Oct 2022

Bibliographical note

41 pages

Keywords

math.AG
math.AT
14F22, 14H52, 14K10, 55N34
Brauer groups
topological modular forms
moduli of elliptic curves
elliptic cohomology

Access to Document

10.48550/arXiv.2210.15743

2210.15743v1Submitted manuscript, 701 KB

Cite this

@techreport{08ae61d251c941f7a4b79ea6f7fada65,

title = "Picard sheaves, local Brauer groups, and topological modular forms",

abstract = " We prove that the Brauer group of TMF is isomorphic to the Brauer group of the derived moduli stack of elliptic curves. Then, we compute the local Brauer group, i.e., the subgroup of the Brauer group of elements trivialized by some \'etale cover of the moduli stack, up to a finite 2-torsion group. ",

keywords = "math.AG, math.AT, 14F22, 14H52, 14K10, 55N34, Brauer groups, topological modular forms, moduli of elliptic curves, elliptic cohomology",

author = "Benjamin Antieau and Lennart Meier and Vesna Stojanoska",

note = "41 pages",

year = "2022",

month = oct,

day = "27",

doi = "10.48550/arXiv.2210.15743",

language = "English",

pages = "1--41",

publisher = "arXiv",

type = "WorkingPaper",

institution = "arXiv",

}

TY - UNPB

T1 - Picard sheaves, local Brauer groups, and topological modular forms

AU - Antieau, Benjamin

AU - Meier, Lennart

AU - Stojanoska, Vesna

N1 - 41 pages

PY - 2022/10/27

Y1 - 2022/10/27

N2 - We prove that the Brauer group of TMF is isomorphic to the Brauer group of the derived moduli stack of elliptic curves. Then, we compute the local Brauer group, i.e., the subgroup of the Brauer group of elements trivialized by some \'etale cover of the moduli stack, up to a finite 2-torsion group.

AB - We prove that the Brauer group of TMF is isomorphic to the Brauer group of the derived moduli stack of elliptic curves. Then, we compute the local Brauer group, i.e., the subgroup of the Brauer group of elements trivialized by some \'etale cover of the moduli stack, up to a finite 2-torsion group.

KW - math.AG

KW - math.AT

KW - 14F22, 14H52, 14K10, 55N34

KW - Brauer groups

KW - topological modular forms

KW - moduli of elliptic curves

KW - elliptic cohomology

U2 - 10.48550/arXiv.2210.15743

DO - 10.48550/arXiv.2210.15743

M3 - Preprint

SP - 1

EP - 41

BT - Picard sheaves, local Brauer groups, and topological modular forms

PB - arXiv

ER -

Picard sheaves, local Brauer groups, and topological modular forms

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this