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

In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…

We present a short proof, based on local character expansions, of the celebrated theorem of Harish-Chandra about local integrability of complex characters of $p$-adic reductive groups. The proof gives an algebraic incarnation of the local…

In local class field theory, the Schmid-Witt symbol encodes interesting data about the ramification theory of $p$-extensi-ons of $K$ and can, for example, be used to compute the higher ramification groups of such extensions. In 1936, Schmid…

In this article we introduce the local versions of the Voevodsky category of motives with Z/p-coefficients over a field k, parameterized by finitely-generated extensions of k. We introduce the, so-called, flexible fields, passage to which…

We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.

This note contains new short proofs of known results on Speh representations of inner forms of $GL_n$ over a local non archimedean field of any characteristic.

In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semi-simple Hopf algebras. A character…

We develop a theory of generalized characters of local systems in $\infty$-categories, which extends classical character theory for group representations and, in particular, the induced character formula. A key aspect of our approach is…

The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…

Let K be a local field of characteristic p with perfect residue field k. In this paper we find a set of representatives for the k-isomorphism classes of totally ramified separable extensions L/K of degree p. This extends work of Klopsch,…

We give a purely cubical argument for the localization theorem for the cubical version of higher Chow groups.

In \cite{D1}, Dickson listed all permutation polynomials up to degree 5 over an arbitrary finite field, and all permutation polynomials of degree 6 over finite fields of odd characteristic. The classification of degree 6 permutation…

We show that Pashin's conjecture on the vanishing of rational higher K-groups of smooth, projective varieties over finite fields can be thought of as a combination of three weaker conjectures.

We introduce the study of parametrized higher category theory and parametrized higher algebra, and we describe the main theorems of the series of Expos\'es that make up the monograph.

In this note we show that the Chern-Simons and the one-loop terms in the M-theory action can be written in terms of new characters involving the M-theory four-form and the string classes. This sheds a new light on the topological structure…

We introduce the tropicalization of closed subschemes of a torus defined over a higher dimensional local field. We study the basic invariants of such tropicalizations. This is a generalization of the results of Einslieder, Kapranov, Lind,…

The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.

Let $G$ be a $p$-adic reductive group with $p$ ``very large.'' For any irreducible admissible representation $\pi$ of $G$ over an algebraically closed field $C$ of characteristic $\not=p$, we define a ``local character expansion'' of $\pi$…

We give a presentation of abelian class field theory.