相关论文: Invitation to higher local fields, Part II, sectio…

We construct a theory of higher local symbols along Parsin chains for reciprocity sheaves. Applying this formalism to differential forms, gives a new construction of the Parsin-Lomadze residue maps, and applying it to the torsion characters…

This note explores the consequences of Koenigsmann's model theoretic argument from the proof of the birational p-adic section conjecture for curves in the context of higher dimensional varieties over p-adic local fields.

This paper introduces a novel approach to the axiomatic theory of quadratic forms. We work internally in a category of certain partially ordered sets, subject to additional conditions which amount to a strong form of local presentability.…

Two-dimensional BF theory with infinitely many higher spin fields is proposed. It is interpreted as the AdS(2) higher spin gravity model describing a consistent interaction between local fields in AdS(2) space including gravitational field,…

For a finite field extension $F/\mathbb{Q}_p$ we associate a coefficient system attached on the Bruhat-Tits tree of $G:= {\rm GL}_2(F)$ to a locally analytic representation $V$ of $G$. This is done in analogy to the work of Schneider and…

It is a survey paper on n-dimensional local fields and adeles on n-dimensional schemes.

We establish a ramified class field theory for smooth projective curves over local fields. As key steps in the proof, we obtain new results in the class field theory for 2-dimensional local fields of positive characteristic, and prove a…

In this short note we prove a formula for local heights on elliptic curves over number fields in terms of intersection theory on a regular model over the ring of integers.

The thesis divides into three parts. The first is devoted to a careful study of very convenient superspace conventions which are a basic tool for the second part. A theorem is formulated that gives a clear statement about when the signs of…

The notion of convexity in tropical geometry is closely related to notions of convexity in the theory of affine buildings. We explore this relationship from a combinatorial and computational perspective. Our results include a convex hull…

Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…

We address a conjecture (referred to as sur in the literature) in the representation theory of a reductive p-adic Lie group G which has important implications for the relationship between mod-p smooth representations and pro-p Iwahori-Hecke…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

In this paper, a new higher Hochschild Complex is defined with an Iterated Integral map to locally model differential forms on the space of bigons on $M$. In particular, given the local data for a gerbe with structure 2-group given by a…

Let $G$ be a higher-rank semisimple Lie group over a nonarchimedean local field, for example $G={\rm PGL}(n,Q_P)$. To any lattice $L$ in $G$ there is an associated simplicial complex $B_L$, given by the quotient by $L$ of the Bruhat-Tits…

I summarize and discuss some recent results on formulating actions of six-dimensional superconformal field theories using the language of higher gauge theory. The latter guarantees mathematical consistency of our constructions and we review…

We consider the special linear group G=SL2 over a p-adic field, and its diagonal subgroup M=GL1. Parabolic induction of representations from M to G induces a map in equivariant homology, from the Bruhat-Tits building of M to that of G. We…

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…

We study the class field theory of curve defined over two dimensional local field. The approch used here is a combination of the work of Kato-Saito, and Yoshida where the base field is one dimensional

These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory, and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of…