Produits dans la cohomologie des variétés arithmétiques : quelques calculs sur les séries thêta
| dc.creator | Bergeron, N. | |
| dc.date | 2006-12-15 | |
| dc.date.accessioned | 2026-07-07T07:35:23Z | |
| dc.date.available | 2026-07-07T07:35:23Z | |
| dc.description | For abelian varieties $A$, in the most interesting cohomology theories $H^* (A)$ is the exterior algebra of $H^1(A)$. In this paper we study a weak generalization of this in the case of arithmetic manifolds associated to orthogonal or unitary groups. In this latter case recall that arithmetic manifolds associated to standard unitary groups $U(p,q)$ ($p\geq q$) over a totally real numberfield have vanishing cohomology in degree $i=1, ..., q-1$ and that, following earlier works of Kazhdan and Shimura, Borel and Wallach constructed in \cite{BorelWallach} non zero degree $q$ cohomology classes. These cohomology classes arise as theta series. After generalizing the construction of these theta series. We prove that arbitrary (up to the obvious obstructions) cup-products of these theta series and their complex conjugates virtually non vanish, i.e. ``up to Hecke translate'', in the cohomology ring. | |
| dc.identifier | https://arxiv.org/abs/math/0612447 | |
| dc.identifier | http://arxiv.org/abs/math/0612447 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120075 | |
| dc.subject | Number Theory | |
| dc.title | Produits dans la cohomologie des variétés arithmétiques : quelques calculs sur les séries thêta | |
| dc.type | text |