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Anabelian aspects in the étale homotopy theory of Brauer-Severi varieties

Schmidt, Johannes

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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.

Item Type: Dissertation
Supervisor: Stix, PD Dr. Jakob
Date of thesis defense: 1 February 2013
Date Deposited: 08 Feb 2013 08:08
Date: 2013
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Mathematics
Subjects: 500 Natural sciences and mathematics
510 Mathematics
Controlled Keywords: Etalhomotopie, Brauer-Severi-Varietät, Anabelsche Geometrie
Uncontrolled Keywords: homotopie rationaler Punkt, homotopie Fixpunkt
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