Inertia groups and abelian surfaces

A. Silverberg; Yu G. Zarhin

doi:10.1016/j.jnt.2004.05.015

Inertia groups and abelian surfaces

A. Silverberg, Yu G. Zarhin

Mathematics

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

6 Scopus citations

Abstract

This paper classifies the finite groups that occur as inertia groups associated to abelian surfaces. These groups can be viewed as Galois groups for the smallest totally ramified extension over which an abelian surface over a local field acquires semistable reduction. The results extend earlier elliptic curves results of Serre and Kraus.

Original language	English (US)
Pages (from-to)	178-198
Number of pages	21
Journal	Journal of Number Theory
Volume	110
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2004.05.015
State	Published - Jan 2005

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2004.05.015

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title = "Inertia groups and abelian surfaces",

abstract = "This paper classifies the finite groups that occur as inertia groups associated to abelian surfaces. These groups can be viewed as Galois groups for the smallest totally ramified extension over which an abelian surface over a local field acquires semistable reduction. The results extend earlier elliptic curves results of Serre and Kraus.",

author = "A. Silverberg and Zarhin, {Yu G.}",

note = "Funding Information: The authors thank B. Eick and P. Brooksbank for help with GAP, K. Lux for helpful comments on an earlier version of the text, I. R. Shafarevich and S.V. Vostokov for useful conversations about the inverse Galois problem, and the referee for helpful comments that improved the final version of the paper. Silverberg thanks the NSA and NSF for financial support.",

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AU - Zarhin, Yu G.

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PY - 2005/1

Y1 - 2005/1

N2 - This paper classifies the finite groups that occur as inertia groups associated to abelian surfaces. These groups can be viewed as Galois groups for the smallest totally ramified extension over which an abelian surface over a local field acquires semistable reduction. The results extend earlier elliptic curves results of Serre and Kraus.

AB - This paper classifies the finite groups that occur as inertia groups associated to abelian surfaces. These groups can be viewed as Galois groups for the smallest totally ramified extension over which an abelian surface over a local field acquires semistable reduction. The results extend earlier elliptic curves results of Serre and Kraus.

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DO - 10.1016/j.jnt.2004.05.015

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SP - 178

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JO - Journal of Number Theory

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Inertia groups and abelian surfaces

Abstract

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