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Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen.  Note For our digital courses all relevant information can be found on the appropriate GRIPS sites.Cohomology of sheaves I SemesterWiSe 2020 / 21 Lecturer Prof. Dr. Guido Kings Type of course (Veranstaltungsart) Vorlesung Contents This is the first part of a two semester course on the cohomology of sheaves. Sheaves are a basic tool in mathematics to describe local-global principles and occur everywhere in mathematics. Typical examples are the continuous functions on a topological space or differentiable forms on a differentiable manifold. Also vector bundles are the same as locally free sheaves of finite rank. To work with sheaves it is important to have a good knowledge of the so called six functor formalism $f_*$, $f^*$, $f_!$, $f^!$, $\otimes$, $Hom$, which works well in the derived category. In view of this, the course will also contain an introduction to derived categories and hence to spectral sequences. An important source of examples for sheaves are equivariant sheaves on locally symmetric spaces, which gives connections to automorphic forms and number theory. The lecture will be divided into two parts: Tuesdays we introduce the general theory and Thursdays we will treat examples. There are no prerequisites besides a good knowledge of the courses Analysis and Algebra of the first four semesters. We plan to treat: Categories, Functors, abelian categories, limits and colimits, sheaves, R-module sheaves, the functors $f_*$, $f^*$, $f_!$, $f^!$, $\otimes$, $Hom$, equivariant sheaves, categories of complexes, the basic notions of triangulated and derived categories and the cohomology of sheaves. The lecture in the summer term will continue with general Poincare-Verdier duality, homotopy invariance of sheaf cohomology, base change, purity, relation to singular and de Rham cohomology, Thom and Chern classes. Besides this we will introduce a purely topological construction of equivariant cohomology classes, which can be expressed by Epstein zeta functions and lead to strong integrality statements for special values of L-functions. Time/Date Tue and Thu 14 - 16 Location digital Course homepage http://www.mathematik.uni-regensburg.de/Mat4/kings/index.html (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MArGeo, MGAGeo, LA-GyGeo ECTS 9 |