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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Galois Categories and Étale Fundamental Groups SemesterSoSe 2026 Lecturer Moritz Kerz, Andrea Panontin, Yuenian Zhou Type of course (Veranstaltungsart) Seminar German title Galois-Kategorien und étale Fundamentalgruppen Contents This reading seminar is devoted to Grothendieck's formalism of Galois categories and étale fundamental groups. Starting from the analogy between classical Galois theory, finite topological covering spaces and finite étale covers of schemes, we will develop the abstract theory of Galois categories and their fundamental groups, and then apply it to the construction and study of the étale fundamental group of a scheme. The aim is to build a conceptual bridge between algebra, topology, and algebraic geometry: after setting up the general Galois category formalism, we will interpret the category of finite étale covers of a scheme as a Galois category, identify its fundamental group with the étale fundamental group, and discuss its basic properties such as homotopy exact sequences, the relation between geometric and arithmetic fundamental groups, comparison with the topological fundamental group over complex field, and specialization in families of schemes. Literature Galois Categories, Anna Cadoret Recommended previous knowledge 1.Category theory: categories, functors, natural transformations, finite limits and colimits, epi/mono, equivalence of categories. 2.Abstract algebra and Galois theory: finite and infinite Galois theory, absolute Galois groups,Krull topology and profinite groups. 3.Basic algebraic geometry: schemes, morphisms of finite type,fibre products and base change. Time/Date Mo, 16:00 - 18:00 Location M 101 Additional question session Time/Date: TBA Location: TBA Course homepage https://elearning.uni-regensburg.de/course/view.php?id=73976 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BSem, MV, MSem, BSem.2 ECTS 4,5 |