Publications

2013

• Construction of automorphic Galois representations II
  
  • Chenevier Gaëtan
  • Harris Michael
  Cambridge Math. Journal, 2013, 1, pp.53-73.
• Hodge theory of the middle convolution
  
  • Dettweiler Michael
  • Sabbah Claude
  Publications of the Research Institute for Mathematical Sciences, European Mathematical Society, 2013, 49 (4), pp.761-800. We compute the behaviour of Hodge data by tensor product with a unitary rank-one local system and middle convolution by a Kummer unitary rank-one local system for an irreducible variation of polarized complex Hodge structure on a punctured complex affine line. We give applications of these formulas to local systems with G_2-monodromy. (10.4171/PRIMS/119)
  DOI : 10.4171/PRIMS/119
• Sur la densite des representations cristallines du groupe de Galois absolu de Q_p
  
  • Chenevier Gaëtan
  Mathematische Annalen, Springer Verlag, 2013, 335, pp.1469-1525. Let X_d be the p-adic analytic space classifying the d-dimensional (semisimple) p-adic Galois representations of the absolute Galois group of Q_p. We show that the crystalline representations are Zarski-dense in many irreducible components of X_d, including the components made of residually irreducible representations. This extends to any dimension d previous results of Colmez and Kisin for d = 2. For this we construct an analogue of the infinite fern of Gouvêa-Mazur in this context, based on a study of analytic families of trianguline (phi,Gamma)-modules over the Robba ring. We show in particular the existence of a universal family of (framed, regular) trianguline (phi,Gamma)-modules, as well as the density of the crystalline (phi,Gamma)-modules in this family. These results may be viewed as a local analogue of the theory of p-adic families of finite slope automorphic forms, they are new already in dimension 2. The technical heart of the paper is a collection of results about the Fontaine-Herr cohomology of families of trianguline (phi,Gamma)-modules.
• ESTIMATES FOR SOLUTIONS OF A LOW-VISCOSITY KICK-FORCED GENERALISED BURGERS EQUATION
  
  • Boritchev Alexandre
  Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, Royal Society of Edinburgh, 2013, pp.143(2), 253-268. We consider a non-homogeneous generalised Burgers equation:$$∂u/∂t + f (u) ∂u/∂x − \nu ∂^2u/∂x^2 = η^ω , t ∈ R, x ∈ S^1 .$$Here, $\nu$ is small and positive, $f$ is strongly convex and satisfies a growth assumption, while $η^ω$ is a space-smooth random "kicked" forcing term. For any solution $u$ of this equation, we consider the quasi-stationary regime, corresponding to $t ≥ 2$. After taking the ensemble average, we obtain upper estimates as well as time-averaged lower estimates for a class of Sobolev norms of $u$. These estimates are of the form $C \nu^{−β}$ with the same values of $β$ for bounds from above and from below. They depend on $η$ and $f$ , but do not depend on the time $t$ or the initial condition.
• Poincaré et la déconstruction du négatif
  
  • Paul Thierry
  , 2013. Nous présentons l'attitude d'Henri Poincaré face aux résultats "négatifs" tels qu'il les a analysés en mécanique céleste et en théorie des quanta.