Related papers: Invitation to higher local fields, Part I, section…

This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…

The authors establish a connection between the Quillen K-theory of certain local fields and the de Rham-Witt complex of their rings of integers with logarithmic poles at the maximal ideal. They consider fields K that are complete discrete…

Let F be a global function field and let F^ab be its maximal abelian extension. Following an approach of D.Hayes, we shall construct a continuous homomorphism \rho: Gal(F^ab/F) \to C_F, where C_F is the idele class group of F. Using class…

These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…

This is a sketch of main steps of the proof of Bloch--Kato's theorem which states that the norm residue homomorphism K_q(K)/m\to H^q(K,\Bbb Z/m(q)) is an isomorphism for a henselian discrete valuation field K of characteristic 0 with…

Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…

A field $K$ is quasi-classical $d$-local if there exist fields $K=k_d,\dots,k_0$ with $k_{i+1}$ Henselian admissible discretely valued with residue field $k_i$, and $k_0$ quasi-finite. We prove a duality theorem for the Galois cohomology of…

As a part of our program for Geometric Arithmetic, we develop an arithmetic cohomology theory for number fields using theory of locally compact groups.

In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.

Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We…

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…

This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts (for part II, see math.AG/0404373). In this first part we investigate a notion of higher topos. For…

We develop local cohomology techniques to study the finite slope part of the coherent cohomology of Shimura varieties. The local cohomology groups we consider are a generalization of overconvergent modular forms, and they are defined by…

Categorial methods for generating new local algebras from old ones are presented. A direct proof of the differential structure of the prolongations of a manifold is proposed.

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be…

We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the…

We introduce a topology, which we call the regional topology, on the space of all real functions on a given locally compact metric space. Next we obtain a new versions of Schauder's fixed point theorem and Ascoli's theorem. We use these…

This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, we relate the k-symplectic and k-cosymplectic manifolds with…

In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…

Suppose $\mathcal K$ is $N$-dimensional local field of characteristic $p$, $\mathcal G =\mathop{Gal}(\mathcal K_{sep}/\mathcal K)$, $\mathcal G_{<p}$ is the maximal quotient of $\mathcal G$ of period $p$ and nilpotent class $<p$ and…