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Deformation of Rigid Conjugate Self-dual Galois Representations
In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a...
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Local to global principle for the moduli space of K3 surfaces
Recently S. Patrikis, J.F. Voloch, and Y. Zarhin have proven, assuming several well-known conjectures, that the finite descent obstruction holds on...
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The Monomial Lattice in Modular Symmetric Power Representations
Let p be a prime. We study the structure of and the inclusion relations among the terms in the monomial lattice in the modular symmetric power...
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On critical values of twisted Artin L-functions
We give a simple proof that critical values of any Artin L -function attached to a representation ϱ with character χ ϱ are stable under twisting by a...
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Classical weight one forms in Hida families: Hilbert modular case
In this paper, we investigate the number of classical weight one specializations of a non-CM ordinary Hida family of parallel weight Hilbert cusp...
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Perfectoid Shimura varieties
This note explains some of the author’s work on understanding the torsion appearing in the cohomology of locally symmetric spaces such as arithmetic...
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Values of twisted Artin L-functions
This note gives a simple proof that certain values of Artin’s L -function, for a representation ρ with character χ ρ , are stable under twisting by an...
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On local Galois representations associated to ordinary Hilbert modular forms
Let F be a totally real field and p be an odd prime which splits completely in F . We show that a generic p -ordinary non-CM primitive Hilbert modular...
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An Octahedral Galois-Reflection Tower of Picard Modular Congruence Subgroups
Between tradition (Hilbert́s 12th Problem) and actual challenges (coding theory) we attack infinite two-dimensional Galois theory. From a number...
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B Sen via distributions on weight space
We introduce a certain ring of rigid-analytic distributions on p -adic weight space (modulo torsion) and show that it is canonically isomorphic to...
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Adequate subgroups II
The notion of adequate subgroups was introduced by Thorne (J Inst Math Jussieu. ar**v:1107.5989,
to appear ). It is a weakening of the notion of big... -
Galois representations for holomorphic Siegel modular forms
We prove local–global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic Hilbert–Siegel modular forms in...
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The image of the coefficient space in the universal deformation space of a flat Galois representation of a p-adic field
The coefficient space is a kind of resolution of singularities of the universal flat deformation space for a given Galois representation of some...
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Algebraic Hecke characters and strictly compatible systems of abelian mod p Galois representations over global fields
In [
10 ] (C R Acad Sci Paris Ser I Math 323(2) 117–120,1996 ), [11 ] (Math Res Lett 10(1):71–832003 ), [12 ] (Can J Math 57(6):1215–12232005 ), Khare... -
Minimal lifts of dihedral 2-dimensional Galois representations
In this paper we study the connection between odd dihedral 2-dimensional modulo p Galois representations and modular forms with complex...