تدریس درس
Algebraic Number Theory
توسط آقای دکتر احسان شاه‌حسینی بصورت آنلاین برای علاقمندان به گرایش نظریه اعداد در دانشگاه رازی.
سرفصل:

Review of basic facts of commutative algebra (like: Noetherian rings and modules, local rings and localization of integral domains, some properties of tensor products), definition of integral elements, proving that integral elements form a ring, ring of integers of a number field and its properties, discriminants, Discrete valuations and Discrete valuation rings, Dedekind domains and UFD property for ideals, the ideal class group, integral closure of Dedekind domains, factorization in extensions, theory of ramification, finding factorizations, norm of ideals, lattices and geometry of numbers, finiteness of class group, Dirichlet’s unit theorem, regulator, CM fields, cyclotomic extensions and their basic properties, regular primes and the first case of Fermat’s last theorem, valuations and absolute values, local fields, nonarchimedean valuations, Ostrowski’s theorem, product formula, weak approximation theorem, completion, Newton’s lemma in nonarchimedean case, Hensel lemma, extensions of nonarchimedean valuations, unramified and totally ramified extensions of local fields, Krasner’s lemma, global fields, decomposition groups, the Frobenius element, statement of Chebotarev density theorem and some of its applications.



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