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arXiv · 1710.06003

On the category of finitely presented mod $p$ representations of $GL_2(F)$

Jack Shotton
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Abstract

Let $F$ be a finite extension of $\mathbb{Q}_p$. We prove that the category of finitely presented smooth $Z$-finite representations of $GL_2(F)$ over a finite extension of $\mathbb{F}_p$ is an abelian subcategory of the category of all smooth representations. The proof uses amalgamated products of completed group rings.

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BibTeXRIS

Jack Shotton. 2017-10-16. On the category of finitely presented mod $p$ representations of $GL_2(F)$. https://doi.org/10.25537/dm.2020v25.143-157

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