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2019 Multiplicity one for wildly ramified representations
Daniel Le
Algebra Number Theory 13(8): 1807-1827 (2019). DOI: 10.2140/ant.2019.13.1807

Abstract

Let F be a totally real field in which p is unramified. Let r̄:GF GL2(F¯p) be a modular Galois representation which satisfies the Taylor–Wiles hypotheses and is generic at a place v above p. Let m be the corresponding Hecke eigensystem. We show that the m-torsion in the modp cohomology of Shimura curves with full congruence level at v coincides with the GL2(kv)-representation D0(r̄|GFv) constructed by Breuil and Paškūnas. In particular, it depends only on the local representation r̄|GFv, and its Jordan–Hölder factors appear with multiplicity one. This builds on and extends work of the author with Morra and Schraen and, independently, Hu–Wang, which proved these results when r̄|GFv was additionally assumed to be tamely ramified. The main new tool is a method for computing Taylor–Wiles patched modules of integral projective envelopes using multitype tamely potentially Barsotti–Tate deformation rings and their intersection theory.

Citation

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Daniel Le. "Multiplicity one for wildly ramified representations." Algebra Number Theory 13 (8) 1807 - 1827, 2019. https://doi.org/10.2140/ant.2019.13.1807

Information

Received: 19 October 2017; Revised: 13 February 2019; Accepted: 27 May 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07118653
MathSciNet: MR4017535
Digital Object Identifier: 10.2140/ant.2019.13.1807

Subjects:
Primary: 11S37

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 8 • 2019
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