The Category of Finitely Presented Smooth Mod pp Representations of GL2(F)GL_2(F)

  • Jack Shotton

    Department of Mathematics, Durham University, Lower Mountjoy, Stockton Road, Durham DH1 3LE, United Kingdom
The Category of Finitely Presented Smooth Mod $p$ Representations of $GL_2(F)$ cover
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Abstract

Let FF be a finite extension of Qp\mathbb{Q}_p. We prove that the category of finitely presented smooth ZZ-finite representations of GL2(F)GL_2(F) over a finite extension of Fp\mathbb{F}_p is an abelian subcategory of the category of all smooth representations. The proof uses amalgamated products of completed group rings.

Cite this article

Jack Shotton, The Category of Finitely Presented Smooth Mod pp Representations of GL2(F)GL_2(F). Doc. Math. 25 (2020), pp. 143–157

DOI 10.4171/DM/741