Period-index bounds for arithmetic threefolds

Benjamin Antieau, Asher Auel, Colin Ingalls, Daniel Krashen, Max Lieblich

Research output: Contribution to journalArticle

Abstract

The standard period-index conjecture for Brauer groups of p-adic surfaces S predicts that ind(α)|per(α)3 for every α∈Br(Qp(S)). Using Gabber’s theory of prime-to-ℓ alterations and the deformation theory of twisted sheaves, we prove that ind(α)|per(α)4 for α of period prime to 6p, giving the first uniform period-index bounds over such fields.

Original languageEnglish (US)
Pages (from-to)301-335
Number of pages35
JournalInventiones Mathematicae
Volume216
Issue number2
DOIs
StatePublished - May 1 2019

Fingerprint

Threefolds
Brauer Group
Deformation Theory
P-adic
Sheaves
Predict

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Antieau, Benjamin ; Auel, Asher ; Ingalls, Colin ; Krashen, Daniel ; Lieblich, Max. / Period-index bounds for arithmetic threefolds. In: Inventiones Mathematicae. 2019 ; Vol. 216, No. 2. pp. 301-335.
@article{63ac1a8dd31647989cce83f2639dc97a,
title = "Period-index bounds for arithmetic threefolds",
abstract = "The standard period-index conjecture for Brauer groups of p-adic surfaces S predicts that ind(α)|per(α)3 for every α∈Br(Qp(S)). Using Gabber’s theory of prime-to-ℓ alterations and the deformation theory of twisted sheaves, we prove that ind(α)|per(α)4 for α of period prime to 6p, giving the first uniform period-index bounds over such fields.",
author = "Benjamin Antieau and Asher Auel and Colin Ingalls and Daniel Krashen and Max Lieblich",
year = "2019",
month = "5",
day = "1",
doi = "10.1007/s00222-019-00860-x",
language = "English (US)",
volume = "216",
pages = "301--335",
journal = "Inventiones Mathematicae",
issn = "0020-9910",
publisher = "Springer New York",
number = "2",

}

Antieau, B, Auel, A, Ingalls, C, Krashen, D & Lieblich, M 2019, 'Period-index bounds for arithmetic threefolds', Inventiones Mathematicae, vol. 216, no. 2, pp. 301-335. https://doi.org/10.1007/s00222-019-00860-x

Period-index bounds for arithmetic threefolds. / Antieau, Benjamin; Auel, Asher; Ingalls, Colin; Krashen, Daniel; Lieblich, Max.

In: Inventiones Mathematicae, Vol. 216, No. 2, 01.05.2019, p. 301-335.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Period-index bounds for arithmetic threefolds

AU - Antieau, Benjamin

AU - Auel, Asher

AU - Ingalls, Colin

AU - Krashen, Daniel

AU - Lieblich, Max

PY - 2019/5/1

Y1 - 2019/5/1

N2 - The standard period-index conjecture for Brauer groups of p-adic surfaces S predicts that ind(α)|per(α)3 for every α∈Br(Qp(S)). Using Gabber’s theory of prime-to-ℓ alterations and the deformation theory of twisted sheaves, we prove that ind(α)|per(α)4 for α of period prime to 6p, giving the first uniform period-index bounds over such fields.

AB - The standard period-index conjecture for Brauer groups of p-adic surfaces S predicts that ind(α)|per(α)3 for every α∈Br(Qp(S)). Using Gabber’s theory of prime-to-ℓ alterations and the deformation theory of twisted sheaves, we prove that ind(α)|per(α)4 for α of period prime to 6p, giving the first uniform period-index bounds over such fields.

UR - http://www.scopus.com/inward/record.url?scp=85060818505&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060818505&partnerID=8YFLogxK

U2 - 10.1007/s00222-019-00860-x

DO - 10.1007/s00222-019-00860-x

M3 - Article

AN - SCOPUS:85060818505

VL - 216

SP - 301

EP - 335

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 2

ER -