R'esolutions flasques des groupes lin'eaires connexes
| dc.creator | Colliot-Th'el`ene, J. -L. | |
| dc.date | 2006-09-19 | |
| dc.date.accessioned | 2026-07-07T07:24:57Z | |
| dc.date.available | 2026-07-07T07:24:57Z | |
| dc.description | A connected reductive group G over a field k may be written as a quotient H/S, where the k-group H is an extension of a quasitrivial torus by a simply connected semisimple group, and S is a flasque k-torus, central in H (a flasque torus is a torus whose cocharacter group is an H^1-trivial Galois lattice). The flasque torus S is well-defined up to multiplication by a quasitrivial torus. Such presentations G=H/S lead to a simplified approach of the Galois cohomology of G and of related objects, such as the Brauer group of a smooth compactification of G. When k is a number field, one also recovers known formulas, in terms of S, for the quotient of the group of rational points by R-equivalence, and for the abelian groups which measure the lack of weak approximation and the failure of the Hasse principle for principal homogeneous spaces. | |
| dc.description | 49 pages, in French | |
| dc.identifier | https://arxiv.org/abs/math/0609521 | |
| dc.identifier | http://arxiv.org/abs/math/0609521 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116566 | |
| dc.subject | Number Theory | |
| dc.subject | Group Theory | |
| dc.subject | 11E72 ; 20G10, 20G15, 20G25, 20G30 | |
| dc.title | R'esolutions flasques des groupes lin'eaires connexes | |
| dc.type | text |