Related papers: Derived class field theory
As it is well-known, Poisson brackets play a fundamental role both in mechanics and in classical field theories. In this paper we develop a theory of extensions of graded Poisson brackets in graded Dirac manifolds. We then show how these…
We study when the derived intersection of two smooth subvarieties of a smooth variety is formal. As a consequence we obtain a derived base change theorem for non-transversal intersections. We also obtain applications to the study of the…
This is a review of Parshin's higher local class field theory in characteristic p.
We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.
We study connections between recollements of the derived category D(Mod-R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature.…
We develop the basic theory of derived quasi-coherent ideals for stacks relative to a given derived algebraic context. We compare different notions of adic completeness with respect to derived ideals, define and compare formal spectra and…
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…
Given an integral domain $D$ with fraction field $F$, its *reciprocal complement* is the subring of $F$ generated by all $1/d$ for nonzero $d$ in $D$. This paper serves doubly as a survey of the current state of the field and an update with…
We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.
Collaboration networks are studied as an example of growing bipartite networks. These have been previously observed to have structure such as positive correlations between nearest-neighbour degrees. However, a detailed understanding of the…
We give a presentation of abelian class field theory.
These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
We develop class field theory of curves over $p$-adic fields which extends the unramified theory of S. Saito. The class groups which approximate abelian \'etale fundamental groups of such curves are introduced in the terms of algebraic…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…
We develop a notion of (principal) differential rank for differential-valued fields, in analog of the exponential rank and of the difference rank. We give several characterizations of this rank. We then give a method to define a derivation…
We construct a fundamental theory of the derived category of non-finite bi-filtered complexes.
The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…
Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support {\tau}-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given…