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Register a new userFormes de Whitney et primitives relatives de formes differentielles sous-analytiques
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Authors
Jean-Paul Brasselet
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Let $X$ be a real-analytic manifold and $gcolon Xto{mathbf R}^n$ a proper triangulable subanalytic map. Given a subanalytic $r$-form $omega$ on $X$ whose pull-back to every non singular fiber of $g$ is exact, we show tha $omega$ has a relative primitive: there is a subanalytic $(r-1)$-form $Omega$ such that $dgLambda (omega-dOmega)=0$. The proof uses a subanalytic triangulation to translate the problem in terms of relative Whitney forms associated to prisms. Using the combinatorics of Whitney forms, we show that the result ultimately follows from the subanaliticity of solutions of a special linear partial differential equation. The work was inspired by a question of Franc{c}ois Treves.
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Let F be a totally real field, v an unramified place of F dividing p and rho a continuous irreducible two-dimensional mod p representation of G_F such that the restriction of rho to G_{F_v} is reducible and sufficiently generic. If rho is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of G_{F_v} in terms of the action of GL_2(F_v) on the cohomology mod p.
Nous montrons que les equations du rep`ere mobile des surfaces de Bonnet conduisent `a une paire de Lax matricielle isomonodromique dordre deux pour la sixi`eme equation de Painleve. We show that the moving frame equations of Bonnet surfaces can be extrapolated to a second order, isomonodromic matrix Lax pair of the sixth Painleve equation.
We proove some inequalities concerning the product, sup * inf for some elliptic operators of order 2 and 4. Using those inequalities and the concentration phenomena we can describe the asymptotic behavior of those PDE solutions.
Let F be a finite extension of Qp, O_F its ring of integers and E a finite extension of Fp. The natural action of the unit group O_F* on O_F extends in a continuous action on the Iwasawa algebra E[[O_F]]. In this work, we show that non zero ideals of E[[O_F]] which are stable under O_F* are open. As a consequence, we deduce the fidelity of the action of E[[U]], with U the subgroup of upper unipotent matrices in GL2(O_F) on an irreducible admissible smooth E-representation of GL2(F). ----- Soit F une extension finie de Qp, danneau des entiers O_F et E une extension finie de Fp. Laction naturelle du groupes des unites O_F* sur O_F se prolonge alors en une action continue sur lalg`ebre dIwasawa E[[O_F]]. Dans ce travail, on demontre que les ideaux non nuls de E[[O_F]] stables par O_F* sont ouverts. En particulier, on en deduit la fidelite de laction de lalg`ebre dIwasawa des matrices unipotentes superieures de GL2(O_F) sur une representation lisse irreductible admissible de GL2(F).
We propose a formula expressing Perron - Frobenius eigenvectors of Cartan matrices in terms of products of values of the Gamma function.
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