Ihara's lemma and level rising in higher dimension

A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Ihara's lemma which is used to rise the modularity property between some congruent galoisian representations. In their work on Sato-Tate, Clozel-Harris-Taylor proposed a generalization of the Ihara's lemma in higher dimension for some similitude groups. The main aim of this paper is then to prove some new instances of this generalized Ihara's lemma by considering some particular non pseudo Eisenstein maximal ideals of unramified Hecke algebras. As a consequence, we prove a level rising statement

Persitence of non degeneracy: a local analog of Ihara's lemma

Persitence of non degeneracy is a phenomenon which appears in the theory of $\overline{\mathbb Q}_l$-representations of the linear group: every irreducible submodule of the restriction to the mirabolic subgroup of an non degenerate irreducible representation is non degenerate. This is no more true in general, if we look at the modulo $l$ reduction of some stable lattice. As in the Clozel-Harris-Taylor generalization of global Ihara's lemma, we show that this property, called non degeneracy persitence, remains true for lattices given by the cohomology of Lubin-Tate spaces

Exact Sparse Matrix-Vector Multiplication on GPU's and Multicore Architectures

We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings \Zb/m\Zb. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve the speed of \spmv{} in the \linbox library, and henceforth the speed of its black box algorithms. Besides, we use this and a new parallelization of the sigma-basis algorithm in a parallel block Wiedemann rank implementation over finite fields

La cohomologie des espaces de Lubin-Tate est libre

This article is the entire version, that is with coefficients in the ring of integers of a local field, of my last paper at inventiones. The principal result is the freeness of the cohomology groups of the Lubin-Tate tower. The strategy is to study the process of saturation in the construction of the filtration of stratification of Harris-Taylor systems local and of the perverse sheaf of vanishing cycles of some unitary Shimura variety. In this new version we use the mirabolic representation and we study the l-torsion of the cockerel between $p$ and $p+$ Harris-Taylor perverse sheaves.Comment: 42 pages, in Frenc

Sur la torsion dans la cohomologie des vari\'et\'es de Shimura de Kottwitz-Harris-Taylor

When the level at $l$ of a Shimura variety of Kottwitz-Harris-Taylor is not maximal, its cohomology with coefficients in a $\overline{\mathbb Z}_l$-local system isn't in general torsion free. In order to prove torsion freeness results of the cohomology, we localize at a maximal ideal $\mathfrak m$ of the Hecke algebra. We then prove a result of torsion freeness resting either on $\mathfrak m$ itself or on the Galois representation $\overline \rho_{\mathfrak m}$ associated to it. Concerning the torsion, in a rather restricted case than the work of Caraiani-Scholze, we prove that the torsion doesn't give new Satake parameters systems by showing that each torsion cohomology class can be raised in the free part of the cohomology of a Igusa variety.Comment: in Frenc