Textbooks and surveys
I.B. Fesenko and S.V. Vostokov, Local Fields and Their Extensions, Second extended edition , AMS 2002, 341 pp.
Invitation to higher local fields, I. Fesenko, M. Kurihara (eds.) Geometry and Topology Monographs vol 3, Warwick 2000
Files of some talks
90 minutes talk on Adelic geometry and analysis on regular models of elliptic curves over global fields and their zeta functions
90 minutes talk on Inter-universal Teichmüller theory of Shinichi Mochizuki
Reciprocity and IUT, talk at RIMS workshop on IUT Summit, July 2016
Adelic lifts of geometry and arithmetic of surfaces and their BSD interaction, talk at EDGE workshop, June 2017
New directions and perspectives in two dimensional number theory I
New directions and perspectives in two dimensional number theory II
New directions and perspectives in two dimensional number theory III
New directions and perspectives in two dimensional number theory IV
Introduction to algebraic number theory
This course (36 hours) is a relatively elementary course which requires minimal prerequisites from commutative algebra for its understanding. Its first part (modules over principal ideal domains, Noetherian modules) follows to a certain extent the book of P. Samuel "Algebraic Theory of Numbers". Then integrality over rings, algebraic extensions of fields, field isomorphisms, norms and traces are discussed in the second part. In the main third part Dedekind rings, factorization in Dedekind rings, norms of ideals, splitting of prime ideals in field extensions, finiteness of the ideal class group and Dirichlet's theorem on units are treated.
This course (25 hours) presents categories, functors, chain complexes, homologies, free, projective and injective objects in the category of modules over a ring, projective and injective resolutions, derived functors, Tor and Ext, cohomologies of modules over a finite group, restriction and corestriction.
Lectures on complete discrete valuation fields
This is a very short introduction to local fields and local class field theory. This course (36 hours) presents basic features of local fields and the local reciprocity map.