Geodesic
The Category of Finitely Presented Smooth Mod $p$ Representations of $GL_2(F)$
Documenta mathematica, Tome 25 (2020), pp. 143-157
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Let F be a finite extension of Qp​. We prove that the category of finitely presented smooth Z-finite representations of GL2​(F) over a finite extension of Fp​ is an abelian subcategory of the category of all smooth representations. The proof uses amalgamated products of completed group rings.
DOI : 10.4171/dm/741
Classification : 11F70, 22E50
Mots-clés : completed group rings, coherent rings, modular representations, smooth admissible representations 
@article{10_4171_dm_741,
     author = {Jack Shotton},
     title = {The {Category} of {Finitely} {Presented} {Smooth} {Mod} $p$ {Representations} of $GL_2(F)$},
     journal = {Documenta mathematica},
     pages = {143--157},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/741},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/741/}
}
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Jack Shotton. The Category of Finitely Presented Smooth Mod $p$ Representations of $GL_2(F)$. Documenta mathematica, Tome 25 (2020), pp. 143-157. doi: 10.4171/dm/741

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