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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Local Class Field Theory SemesterSoSe 2026 Lecturer Shai Keidar Type of course (Veranstaltungsart) Vorlesung German title Lokale Klassenkörpertheorie Contents Class field theory gives an intrinsic description of all abelian Galois extensions of a given field. The case of the rational numbers appears very early: the roots of the polynomials X^n ? 1 generate abelian Galois extensions of the rationals. It is, however, far from obvious that essentially all abelian extensions of the rationals arise in this way. No analogous explicit description is known for a general number field. In contrast, over a complete local field such as the p-adic numbers, the situation is much better. The theory of Lubin–Tate formal groups provides a systematic method for producing equations whose roots generate all abelian extensions of the field. Literature Milne, Class Field Theory; Emily Riehl, Lubin-Tate Formal Groups and Local Class Field Theory - Bachelor's thesis; Serre, Local Fields Recommended previous knowledge basic algebra, including Galois theory. Previous encounter with p-adic numbers is helpful but not strictly necessary. Time/Date Mon 10-12; Wed 12-14; Exercises: Fri 10-12 Location Mon M101; Wed M103; Exercises: M009 Course homepage https://www.shaikeidar.com/teaching/cft-2026 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BAlg(2), BV, MV, MArGeo, LA-GyAlg ECTS 9 |