Quasi-semi-stable representations
By Xavier Caruso, Tongyin Liu. 2007
57 citations recorded by the source corpus.
Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of p-adic torsion representations of G_\infty, named quasi-semi-stable. We prove that these representations are "explicitly" described by a certain category of linear algebra objects. The results of this note should be consider as a first step in the understanding of the structure of quotients of two lattices in a crystalline (resp. semi-stable) Galois representation.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dfb4de69a19875a4fe2e5c8a0301126ae22fabe3
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the weights of mod p Hilbert modular forms (2006, methodology): “:= gf(bg −1 (x)), where gis the image of gin Gal(K/K0), and the action of Gal(K/K0) on Aˆ = AˆKis defined in section 4.2 of [Car09]. For the compatibility of this definition with those used in [Bre99], [CL09] and [Sav05], see Lemma 3.3.1.2 of [Bre98]. This functor is exact and faithful, and preserves ”
- On lattices in semi-stable representations: a proof of a conjecture of Breuil (2008, unknown): “In fact, the functor M S can be proved to be an equivalence [CL07].”