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Let p be a prime number and f an overconvergent p-adic automorphic form on a definite unitary group which is split at p. Assume that f is of classical weight and that its Galois representation is crystalline at places dividing p, then f is conjectured to be a classical automorphic form. We prove new cases of this conjecture in arbitrary dimension by making crucial use of the patched eigenvariety.
We construct parabolic analogues of (global) eigenvarieties, of patched eigenvarieties and of (local) trianguline varieties, that we call respectively Bernstein eigenvarieties, patched Bernstein eigenvarieties, and Bernstein paraboline varieties. We
Let $F$ be a totally real field in which $p$ is unramified. We prove that, if a cuspidal overconvergent Hilbert cuspidal form has small slopes under $U_p$-operators, then it is classical. Our method follows the original cohomological approach of Cole
Let $F$ be a quadratic real field, $p$ be a rational prime inert in $F$. In this paper, we prove that an overconvergent $p$-adic Hilbert eigenform for $F$ of small slope is actually a classical Hilbert modular form.
Let F be a global field and A its ring of adeles. Let G:=SL(2). We study the bilinear form B on the space of K-finite smooth compactly supported functions on G(A )/G(F) defined by the formula B (f,g):=B(f,g)-(M^{-1}CT (f),CT (g)), where B is the usua
We prove the isogeny property for special fibres of integral canonical models of compact Shimura varieties of $A_n$, $B_n$, $C_n$, and $D_n^{dbR}$ type. The approach used also shows that many crystalline cycles on abelian varieties over finite fields