Descente de torseurs, gerbes et points rationnels - Descent of torsors, gerbes and rational points
| dc.creator | Zahnd, Stephane | |
| dc.date | 2004-01-14 | |
| dc.date | 2004-01-16 | |
| dc.date.accessioned | 2026-07-07T05:04:31Z | |
| dc.date.available | 2026-07-07T05:04:31Z | |
| dc.description | Let $k$ be a field of characteristic 0 and $G$ a linear algebraic $k$-group. When $G$ is abelian, it is well known that torsors under $G_{X}$ over a $k$-scheme $π:X\to \textup{Spec} k$ provide an obstruction to the existence of $k$-rational points on $X$, since Leray spectral sequence gives rise (when $X$ is 'nice', e.g. $X$ smooth and proper) to an exact sequence of groups (5-term exact sequence associated). This sequence gives an obstruction for a $\bar{G}_{X}$-torsor $\bar{P}\to\bar{X}$ with field of moduli $k$ to be defined over $k$, i.e. to be obtained by extension of scalars to the algebraic closure $\bar{k}$ of $k$ from a $G_{X}$-torsor $P\to X$. This obstruction is measured by a gerbe, which is neutral if $X$ possesses a $k$-rational point. We try to extend this result to the non-commutative case, and in some cases, we deduce non-abelian cohomological obstruction to the existence of $k$-rational points on $X$, and results about descent of torsors. | |
| dc.description | 144 pages, uses xypic, in french, thesis | |
| dc.identifier | https://arxiv.org/abs/math/0401140 | |
| dc.identifier | http://arxiv.org/abs/math/0401140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69835 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14G05, 14A20, 14F20, 18G50 | |
| dc.title | Descente de torseurs, gerbes et points rationnels - Descent of torsors, gerbes and rational points | |
| dc.type | text |