TY  - GEN
TI  - Anabelian aspects in the étale homotopy theory of Brauer-Severi varieties
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/14452/
ID  - heidok14452
N2  - We study the étale homotopy theory of Brauer-Severi varieties over fields of characteristic 0.
We prove that the induced Galois representations on geometric homotopy invariants (e.g., l-adic cohomology or higher homotopy groups) are all isomorphic for Brauer-Severi varieties of the same dimension.
If the base field has cohomological dimension smaller or equal 2 then we can show more in the case of Brauer-Severi curves:
There is even an isomorphism between the Hochschild-Serre spectral sequences computing cohomology with local coefficients.
Further, we study homotopy rational and homotopy fixed points on Brauer-Severi varieties and their connections to genuine rational points.
In particular, we show that under a suitable assumption on the first profinite Chern class map an analogue of the weak section conjecture for Brauer-Severi varieties turns out to be true.
We can give a counter example to this analogue without the extra assumption over p-adic local fields.

KW  - homotopie rationaler Punkt
KW  -  homotopie Fixpunkt
AV  - public
A1  - Schmidt, Johannes
Y1  - 2013///
ER  -