Shotton, Jack

The Category of Finitely Presented Smooth Mod \(p\) Representations of \(GL_2(F)\)

Doc. Math. 25, 143-157 (2020)
DOI: 10.25537/dm.2020v25.143-157
Communicated by Otmar Venjakob

Summary

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.

Mathematics Subject Classification

22E50, 11F70

Keywords/Phrases

completed group rings, coherent rings, modular representations, smooth admissible representations

References

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Affiliation

Shotton, Jack
Department of Mathematics, Durham University, Lower Mountjoy, Stockton Road, Durham DH1 3LE, United Kingdom

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