Back to Search
Start Over
Sur la torsion dans la cohomologie des vari\'et\'es de Shimura de Kottwitz-Harris-Taylor
- Source :
- Journal of the Institute of Mathematics of Jussieu 2017 pp 1-19
- Publication Year :
- 2015
-
Abstract
- 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.<br />Comment: in French
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Language :
- French
- Database :
- arXiv
- Journal :
- Journal of the Institute of Mathematics of Jussieu 2017 pp 1-19
- Publication Type :
- Report
- Accession number :
- edsarx.1503.03303
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/S1474748017000093