Related papers: Invitation to higher local fields (Introduction)

This work presents author's explicit methods of constructing abelian extensions of complete discrete valuation fields. His approach to explicit equations of a cyclic extension of degree p^n which contains a given cyclic extension of degree…

This is an introduction to noncommutative local reciprocity maps for totally ramified Galois extensions with arithmetically profinite group. These maps in general are not homomorphisms but Galois cycles; a description of their image and…

A main problem in Galois theory is to characterize the fields with a given absolute Galois group. We apply a K-theoretic method for constructing valuations to study this problem in various situations. As a first application we obtain an…

This is an expanded version of the author's lecture at the Conference in Commutative Algebra and Algebraic Geometry in Messina Italy in June 1999. The purpose of the talk was to give a brief introduction to the subject of tight closure,…

This is a collection of my lecture notes on the higher-spin theory course given for students at the Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University. The goal of these lectures is to give an introduction…

Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of…

This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…

Talk given at the conference "Visions in Mathematics toward the year 2000", August 1999, Tel-Aviv.

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

This is a review of the vast area of explicit formulas for the (wild) Hilbert symbol (not only in the one-dimensional case but in the higher dimensional case as well). An extensive bilbiography is included.

This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.

These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…

This is is a survey of applications of Fontaine's theory of p-adic representations of local fields (Phi-Gamma-modules) to Galois cohomology of local fields and explicit formulas for the Hilbert symbol in relation with two-dimensional local…

This is an introduction to the author theory of cyclic p-extensions of an absolutely unramified complete discrete valuation field K with arbitrary residue field of characteristic p. In this theory a homomorphism is constructed from the…

This monograph is derived from a series of six lectures I gave at the Centre de Recherches Mathematiques in Montreal, in March and June 2000, while titulary of the Aisenstadt Chair.

This work sketches the author classification of complete discrete valuation fields K of characteristic 0 with residue field of characteristic p into two classes depending on the behaviour of the torsion part of a differential module. For…

This set of lecture notes on local theta correspondence is the written version of a mini-course the author gave in March of 2025 for the program ``Representation Theory and Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris.…

Summary talk at ICHEP 2002, Amsterdam, July 2002. I have kept very close to the content and style of the talk as it was delivered. You may access the associated PowerPoint presentation through a link at…

The present informal set of notes covers the material that has been presented by the author in a series of lectures for the Doctoral School in Mathematics of the Southern Federal State University of Rostov-on-Don in the Fall of 2020 and…