Finiteness properties of the category of mod p representations of

We establish the Bernstein-centre type of results for the category of mod p representations of $\operatorname {\mathrm {GL}}_2 (\mathbb {Q}_p)$ . We treat all the remaining open cases, which occur when p is $2$ or $3$ . Our arguments carry over for all primes p . This allows us to remove the restric...

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Published in:Forum of mathematics. Sigma 2021-12, Vol.9, Article e80
Main Authors: Paškūnas, Vytautas, Tung, Shen-Ning
Format: Article
Language:English
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Summary:We establish the Bernstein-centre type of results for the category of mod p representations of $\operatorname {\mathrm {GL}}_2 (\mathbb {Q}_p)$ . We treat all the remaining open cases, which occur when p is $2$ or $3$ . Our arguments carry over for all primes p . This allows us to remove the restrictions on the residual representation at p in Lue Pan’s recent proof of the Fontaine–Mazur conjecture for Hodge–Tate representations of $\operatorname {\mathrm {Gal}}(\overline {\mathbb Q}/\mathbb {Q})$ with equal Hodge–Tate weights.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2021.72