2020/08/31 by Michael Fütterer, Fütterer, Michael, José Villanueva +1
Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Mathematics #Historical and socio-economic studies of Spain and related regions #Humanities #Number Theory (math.NT) #Philosophy #Political science #Social Sciences and Policies #math.NT
paper · pdf · doi:10.48550/arxiv.2008.13375
in Spanish
arxiv created 2020/08/31 · openalex publication_date 2020/08/31 · arxiv updated 2020/09/01 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/28
This text is a mostly self-contained textbook-like introduction to classical and modern Iwasawa Theory in Spanish language. It grew out of notes for a course that the authors gave at the annual conference of the Mexican Mathematical Society (SMM) in 2018. It covers some preliminaries from algebraic number theory and profinite algebra, the theory of the Iwasawa algebra and its modules, results about class groups in ℤp-extensions, p-adic L-functions for Dirichlet characters and their various constructions (along with some complex theory of L-functions), the cyclotomic main conjecture in different formulations together with its most important implications, and a chapter about generalizations outlining logarithmic Iwasawa theory and generalizations of the Main conjecture to elliptic curves, motives and the ETNC. The text includes references and detailed proofs, some of which are not available in the standard literature, and is accessible for anyone with basic knowledge of algebra and some algebraic number theory.