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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. In the course we will develop its main tools that are connected to algebraic integers, prime ideals,
ideal class group, unit group, and subgroups of the Galois group, including basics of p-adic numbers and
applications to Diophantine equations.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (07.12.2018)
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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. (16.02.2023)
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James A. Milne, Algebraic Number Theory, online.
Serge Lang, Algebraic Number Theory, GTM 110, 1994.
E.I. Borevič, I.R. Šafarevič: Number Theory, Academic Press 1966.
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. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (07.12.2018)
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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. (16.02.2023)
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Algebraic integers Dedekind domains Prime factorization, ramification and splitting Geometry of numbers, Minkowski bound Finiteness of class group Dirichlet unit theorem, regulator Cyclotomic fields, Diophantine equations p-adic numbers Ramification and inertia group, Frobenius element Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (07.12.2018)
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