Subgroups of Inertia Groups Arising from Abelian Varieties

A. Silverberg; Yu G. Zarhin

doi:10.1006/jabr.1998.7523

Subgroups of Inertia Groups Arising from Abelian Varieties

A. Silverberg, Yu G. Zarhin

Mathematics

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

9 Scopus citations

Abstract

Given an abelian variety over a field with a discrete valuation, Grothendieck defined a certain open normal subgroup of the absolute inertia group. This subgroup encodes information on the extensions over which the abelian variety acquires semistable reduction. We study this subgroup, and use it to obtain information on the extensions over which the abelian variety acquires semistable reduction.

Original language	English (US)
Pages (from-to)	94-107
Number of pages	14
Journal	Journal of Algebra
Volume	209
Issue number	1
DOIs	https://doi.org/10.1006/jabr.1998.7523
State	Published - Nov 1 1998

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1006/jabr.1998.7523

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title = "Subgroups of Inertia Groups Arising from Abelian Varieties",

abstract = "Given an abelian variety over a field with a discrete valuation, Grothendieck defined a certain open normal subgroup of the absolute inertia group. This subgroup encodes information on the extensions over which the abelian variety acquires semistable reduction. We study this subgroup, and use it to obtain information on the extensions over which the abelian variety acquires semistable reduction.",

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

note = "Funding Information: The authors thank Karl Rubin for helpful conversations. Zarhin thanks NSF for financial support. Silverberg thanks NSA and the Science Scholars Fellowship Program at the Bunting Institute for financial support.",

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N2 - Given an abelian variety over a field with a discrete valuation, Grothendieck defined a certain open normal subgroup of the absolute inertia group. This subgroup encodes information on the extensions over which the abelian variety acquires semistable reduction. We study this subgroup, and use it to obtain information on the extensions over which the abelian variety acquires semistable reduction.

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Subgroups of Inertia Groups Arising from Abelian Varieties

Abstract

All Science Journal Classification (ASJC) codes

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