Related papers: Notes on abelian class field theory
We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…
We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.
We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.
This note proposes a new notion of a gradient-like vector field and discusses its implications for the theory of Stein and Weinstein structures.
We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
We extend to logarithmic class groups the results on abelian principalization of tame ray class groups of a number field obtained in a previous article.
In this paper we describe all gradings by abelian groups without elements of order p, where p > 2 is the characteristic of the base field, on the simple graded Cartan type Lie algebras.
Author's generalization of one-dimensional class field theory to theory of abelian totally ramified p-extensions of a complete discrete valuation field with arbitrary non-separably p-closed residue field and its applications are described.
In this mostly expository note, we explain a proof of Tate's two conjectures [Tat65] for algebraic cycles of arbitrary codimension on certain products of elliptic curves and abelian surfaces over number fields.
This is a pedagogical introduction to the treatment of general relativity as a quantum effective field theory. Gravity fits nicely into the effective field theory description and forms a good quantum theory at ordinary energies.
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…
We develop a notion of degree for functions between two abelian groups that allows us to generalize the Chevalley Warning Theorems from fields to noncommutative rings or abelian groups of prime power order.
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
We survey the theory of absolute Hodge classes. The notes include a full proof of Deligne's theorem on absolute Hodge classes on abelian varieties as well as a discussion of other topics, such as the field of definition of Hodge loci and…
An overview of the accomplishments of constructive quantum field theory is provided.
Lenstra introduced the notion of the Euclidean ideal class, a generalization of the Euclidean domain that captures cyclic class groups. In this article, we establish the existence of Euclidean ideal classes in abelian quartic fields. As a…
These are lecture notes expanding upon a set of lectures given by G.M. at the TASI 2023 School. Part I is an introduction to topological field theory, including extended topological field theory. Part II is an introduction to generalized…