Finiteness of unramified deformation rings

Patrick B. Allen; Frank Calegari

doi:10.2140/ant.2014.8.2263

Finiteness of unramified deformation rings

Patrick B. Allen
, Frank Calegari

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

Abstract

We prove that the universal unramified deformation ring R^unr of a continuous Galois representation (formula displayed) (for a totally real field F⁺ and finite field k) is finite over O = W(k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring R^univ is finite over the local deformation ring R^loc.

Original language	English (US)
Pages (from-to)	2263-2272
Number of pages	10
Journal	Algebra and Number Theory
Volume	8
Issue number	9
DOIs	https://doi.org/10.2140/ant.2014.8.2263
State	Published - 2014
Externally published	Yes

Keywords

Galois representations

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.2140/ant.2014.8.2263

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title = "Finiteness of unramified deformation rings",

abstract = "We prove that the universal unramified deformation ring Runr of a continuous Galois representation (formula displayed) (for a totally real field F+ and finite field k) is finite over O = W(k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring Runiv is finite over the local deformation ring Rloc.",

keywords = "Galois representations",

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year = "2014",

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AU - Allen, Patrick B.

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AB - We prove that the universal unramified deformation ring Runr of a continuous Galois representation (formula displayed) (for a totally real field F+ and finite field k) is finite over O = W(k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring Runiv is finite over the local deformation ring Rloc.

KW - Galois representations

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UR - https://www.scopus.com/pages/publications/84928168825#tab=citedBy

U2 - 10.2140/ant.2014.8.2263

DO - 10.2140/ant.2014.8.2263

M3 - Article

AN - SCOPUS:84928168825

SN - 1937-0652

VL - 8

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JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 9

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Finiteness of unramified deformation rings

Abstract

Keywords

ASJC Scopus subject areas

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