Geodesic
The Category of Finitely Presented Smooth Mod $p$ Representations of $GL_2(F)$
Documenta mathematica, Tome 25 (2020), pp. 143-157.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 22E50, 11F70
Keywords: completed group rings, coherent rings, modular representations, smooth admissible representations 
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     author = {Shotton, Jack},
     title = {The {Category} of {Finitely} {Presented} {Smooth} {Mod} \(p\) {Representations} of {\(GL_2(F)\)}},
     journal = {Documenta mathematica},
     pages = {143--157},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a66/}
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Shotton, Jack. The Category of Finitely Presented Smooth Mod \(p\) Representations of \(GL_2(F)\). Documenta mathematica, Tome 25 (2020), pp. 143-157. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a66/