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Algebraic number theory studies the structure of number fields and forms the basis for most of advanced areas of
number theory. Following the lecture Basic algebraic number theory (NMAG472) we will study more advanced
topics, in particular (prime) ideals in general Dedekind domains, p-adic numbers and local fields, subgroups of
the Galois group, and adeles and applications of class field theory.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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The course requires an oral exam and credit for the exercises. The credit for the exercises "zapocet" will be awarded for successfully solving several sets of homework problems. Zapocet is not needed for taking the exam. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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H. Cohen, A course in computational algebraic number theory, Springer-Verlag, Berlin 1996.
A. Frőhlich, M. J. Taylor, Algebraic number theory, Cambridge University Press, Cambridge 1991.
Daniel A. Marcus, Number Fields, Universitext, 2018.
James A. Milne, Algebraic Number Theory, online.
James A. Milne, Class Field Theory, online.
Serge Lang, Algebraic Number Theory, GTM 110, 1994. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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The exam is oral with approx. 60 minutes time for preparation for 1 or 2 questions corresponding to the material covered by the course. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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Dedekind domains Prime factorization, ramification and splitting p-adic numbers, local fields Ramification and inertia group, Frobenius element Adeles and ideles Main theorems of class field theory, Hilbert class field, Artin map Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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