Semistable abelian varieties and maximal torsion 1-crystalline submodules

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Semistable abelian varieties and maximal torsion 1-crystalline submodules. / Gunton, Cody.

In: Journal de Theorie des Nombres de Bordeaux, Vol. 33, No. 1, 2021, p. 39-81.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Gunton, C 2021, 'Semistable abelian varieties and maximal torsion 1-crystalline submodules', Journal de Theorie des Nombres de Bordeaux, vol. 33, no. 1, pp. 39-81. https://doi.org/10.5802/JTNB.1151

APA

Gunton, C. (2021). Semistable abelian varieties and maximal torsion 1-crystalline submodules. Journal de Theorie des Nombres de Bordeaux, 33(1), 39-81. https://doi.org/10.5802/JTNB.1151

Vancouver

Gunton C. Semistable abelian varieties and maximal torsion 1-crystalline submodules. Journal de Theorie des Nombres de Bordeaux. 2021;33(1):39-81. https://doi.org/10.5802/JTNB.1151

Author

Gunton, Cody. / Semistable abelian varieties and maximal torsion 1-crystalline submodules. In: Journal de Theorie des Nombres de Bordeaux. 2021 ; Vol. 33, No. 1. pp. 39-81.

Bibtex

@article{63084a4e61d44ac6b76b95bf42c6eb8d,
title = "Semistable abelian varieties and maximal torsion 1-crystalline submodules",
abstract = "Let p be a prime, let K be a discretely valued extension of Qp, and let AK be an abelian K-variety with semistable reduction. Extending work by Kim and Marshall from the case where p > 2 and K/Qp is unramified, we prove an l = p complement of a Galois cohomological formula of Grothendieck for the l-primary part of the N{\'e}ron component group of AK . Our proof in-volves constructing, for each m ∈ Z≥0, a finite flat OK-group scheme with generic fiber equal to the maximal 1-crystalline submodule of AK [pm ]. As a corollary, we have a new proof of the Coleman–Iovita monodromy criterion for good reduction of abelian K-varieties.",
keywords = "Log 1-motive, N{\'e}ron component group, Torsion 1-crystalline representation",
author = "Cody Gunton",
note = "Publisher Copyright: {\textcopyright} Soci{\'e}t{\'e} Arithm{\'e}tique de Bordeaux, 2021, tous droits r{\'e}serv{\'e}s.",
year = "2021",
doi = "10.5802/JTNB.1151",
language = "English",
volume = "33",
pages = "39--81",
journal = "Journal de Theorie des Nombres de Bordeaux",
issn = "1246-7405",
publisher = "Universite de Bordeaux I Centre de Recherces en Mathematiques",
number = "1",

}

RIS

TY - JOUR

T1 - Semistable abelian varieties and maximal torsion 1-crystalline submodules

AU - Gunton, Cody

N1 - Publisher Copyright: © Société Arithmétique de Bordeaux, 2021, tous droits réservés.

PY - 2021

Y1 - 2021

N2 - Let p be a prime, let K be a discretely valued extension of Qp, and let AK be an abelian K-variety with semistable reduction. Extending work by Kim and Marshall from the case where p > 2 and K/Qp is unramified, we prove an l = p complement of a Galois cohomological formula of Grothendieck for the l-primary part of the Néron component group of AK . Our proof in-volves constructing, for each m ∈ Z≥0, a finite flat OK-group scheme with generic fiber equal to the maximal 1-crystalline submodule of AK [pm ]. As a corollary, we have a new proof of the Coleman–Iovita monodromy criterion for good reduction of abelian K-varieties.

AB - Let p be a prime, let K be a discretely valued extension of Qp, and let AK be an abelian K-variety with semistable reduction. Extending work by Kim and Marshall from the case where p > 2 and K/Qp is unramified, we prove an l = p complement of a Galois cohomological formula of Grothendieck for the l-primary part of the Néron component group of AK . Our proof in-volves constructing, for each m ∈ Z≥0, a finite flat OK-group scheme with generic fiber equal to the maximal 1-crystalline submodule of AK [pm ]. As a corollary, we have a new proof of the Coleman–Iovita monodromy criterion for good reduction of abelian K-varieties.

KW - Log 1-motive

KW - Néron component group

KW - Torsion 1-crystalline representation

UR - http://www.scopus.com/inward/record.url?scp=85107734794&partnerID=8YFLogxK

U2 - 10.5802/JTNB.1151

DO - 10.5802/JTNB.1151

M3 - Journal article

AN - SCOPUS:85107734794

VL - 33

SP - 39

EP - 81

JO - Journal de Theorie des Nombres de Bordeaux

JF - Journal de Theorie des Nombres de Bordeaux

SN - 1246-7405

IS - 1

ER -

ID: 276954198