Ruprecht-Karls-Universität Heidelberg
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„Vector Bundles over Rigid Analytic Varieties“
Helene Sigloch, Universität Freiburg

Classification of vector bundles has always been a popular problem all over geometry. Grauert (1957) classified holomorphic vector bundles on Stein spaces up to isomorphism by homotopy classes of maps into the infinite Grassmannian. Morel (2012) classsified algebraic vector bundles on smooth affine varieties up to isomorphism by A¹-homotopy classes into the infinite Grassmannian. I want to do the same for vector bundles over rigid analytic varieties. Using a trick of Schlichting's, Asok-Hoyois-Wendt managed to and considerably generalise Morel's theorem and simplify the proof. Transferring their technique to the rigid analytic setting, I could prove that isomorphism classes of line bundles correspond to rigid analytic A¹-homotopy classes to a classifying space. In the talk I will give a short introduction into rigid analytic varieties and affinoid algebras. I will explain the question and give the known results, focusing on the difference between the algebro-geometric and the rigid analytic setting.

Freitag, den 22. Januar 2016 um 13:30 Uhr, in INF288, HS2 Freitag, den 22. Januar 2016 at 13:30, in INF288, HS2

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Alexander Schmidt