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Local class field theory with formal modules SemesterSoSe 2023 Lecturer Niko Naumann Type of course (Veranstaltungsart) Vorlesung German title Lokale Klassenkörpertheorie mit formalen Moduln Contents Class field theory gives an intrinsic description of all abelian Galois extensions of a given field. The class field theory of the rationals is encounter very early on: roots of the polynomials X^n-1=0 generate abelian Galois extensions of the rationals, though it is hard to see, that in fact essentailly all such extensions are obtained. There is no known such description for a general number field in place of the rationals However, over a complete local field like the p-adic numbers, the situation is much better: The theory of Lubin-Tate modules provides a way of systematically producing equations the roots of which generate all abelian extensions. Literature see GRIPS Recommended previous knowledge basic algebra, including Galois theory. Previous encounter with p-adics is helpful but not strictly necessary, as we will provide a review of this. Time/Date Wed, 4-6 pm H31 and Fri, 10-12 am, H32 Location excersise class: Fri, 12-2 pm, M101 Course homepage https://elearning.uni-regensburg.de/course/view.php?id=60081 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BAlg(2), BV, MV, MArGeo, LA-GyAlg ECTS 9 |