Overconvergent modular forms and the Fontaine-Mazur conjecture

By M. Kisin. 2003

206 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eccb036b31f240aba7607464f11eb23f6f53994b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the infinite fern of Galois representations of unitary type (2009, background): “lemma. Up to enlarging B if necessary, we may find a compact open subgroup K U(AF,S0) cutting exactly the union of components B, in the sense that an irreducible representation of U(AF,S0) belongs to B if, and only if, K 6= 0.”
An introduction to the theory of p-adic representations (2002, background): “XJ,cris is a closed subspace of X. More generally, one can show that for any K, the spaces XJ,cris, XJ,st and XJ,dR are all analytic subspaces of X. All of this is work in progress with Colmez. Kisin [60] has interesting results on families of p-adic representations. ♦♠♥♣ 38 VI. Appendix VI.1. Diagr”
Potential automorphy and change of weight (2010, methodology): “k(℘) H 0(G K,adρ℘) = n2 +dim k(℘) H 2(G K,adρ℘) = n2 +dim k(℘) H 0(G K,(adρ℘)(1)), by the local Euler characteristic formula for Ql-modules and local duality for Qlmodules. (The proof of Lemma 9.7 of [Kis03] shows that the usual Euler characteristic formula with ﬁnite coeﬃcients implies the analogou”
Symmetric power functoriality for holomorphic modular forms, II (2020, background): “require a restriction to cusp forms of level 1 – see Theorem 2.30. It is based on an inﬁnitesimal R= T theorem on the eigenvariety associated to a deﬁnite unitary group in nvariables. Kisin (for GL2) [Kis03] and Bellaiche–Chenevier (for higher rank) [BC09] have observed that such theorems are often ”
On the eigencurve at classical weight $1$ points (2013, background): “This result has been generalized to all non-critical classical points of weight two or more by Coleman and Mazur [9], when the tame level is one, and by Kisin [14] for arbitrary tame level.”
Classification of two-dimensional split trianguline representations of p-adic fields (2008, methodology): “adic representations of GQpattached to ﬁnite slope overconvergent modular forms are trianguline, this fact was a key for his p-adic Hodge theoretic approach to the study of Coleman-Mazur eigencurves ([Ki03]). Recently Bella¨ıche-Chenevier generalized Kisin’s method and studied higher dimensional tri”
Cohomology and Duality for (φ, Γ)-modules over the Robba Ring (2007, background): “(The supply of such representations is plentiful: for instance, a result of Kisin [20] implies that many of the Galois representations associated to overconvergent p-adic modular forms are trianguline.”
Triangulation of refined families (2012, background): “In [20], Kisin proved the Fontaine-Mazur conjecture for Galois representations attached to finite slope, overconvergent p-adic cuspidal eigenforms.”
Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality (2014, background): “ is nonzero for each 1 ≤ i≤ n, where χ v: GFv → O×is the Lubin-Tate character associated with our chosen uniformizer v. Part iii. of this conjecture is naturally inspired by a famous result of Kisin [Kis03] and its generalizations due to Bellaïche-Chenevier, Hellmann and others [BC09, Hel12]. When F”