Related papers: Normed Fiber Functors

Following Lusztig and Vogan, we study the Bruhat $G$-order on the set $\mathcal{D}$ of rank $1$ local systems on $B$-orbits over an Hermitian symmetric variety $G/L$. The main aim is to give a combinatorial characterization similar to the…

Let F be a local henselian nonarchimedean field of residual field k, and let G be the group of F-points of a connected reductive group defined over F. It is well-known that the quotient of any parahoric subgroup of G by its first congruence…

In the case where $G=$SL$_{2}(F)$ for a non-archimedean local field $F$ and $\Gamma$ is a discrete torsion-free cocompact subgroup of $G$, there is a known relationship between the Ihara zeta function for the quotient of the Bruhat-Tits…

For a profinite group $G$ we describe an abelian group $W_G(R; M)$ of $G$-typical Witt vectors with coefficients in an $R$-module $M$ (where $R$ is a commutative ring). This simultaneously generalises the ring $W_G(R)$ of Dress and…

We argue that M-theory compactified on an arbitrary genus-one fibration, that is, an elliptic fibration which need not have a section, always has an F-theory limit when the area of the genus-one fiber approaches zero. Such genus-one…

In our previous paper "Bruhat-Tits theory from Berkovich's point of view. I ? Realizations and compactifications of buildings", we investigated realizations of the Bruhat-Tits building B(G,k) of a connected and reductive linear algebraic…

By an $\ell$-group $G$ we mean a lattice-ordered abelian group. This paper is concerned with the category $\FP$ of finitely presented {\it unital} $\ell$-groups, those $\ell$-groups having a distinguished order-unit $u$. Using the duality…

We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated with a fibration of pointed groupoids. Our generalization…

In this article we formulate and prove the analogue of the Langlands-Rapoport conjecture for the moduli stacks of global $G$-shtukas. Here $G$ is a parahoric Bruhat-Tits group scheme over a smooth projective curve $C$ over a finite field…

In this paper, we prove that a normal subgroup N of an n-dimensional crystallographic group G determines a geometric fibered orbifold structure on the flat orbifold E^n/G, and conversely every geometric fibered orbifold structure on E^n/G…

We construct $p$-adic analogs of operator colligations and their characteristic functions. Consider a $p$-adic group $G=GL(\alpha+k\infty, Q_p)$, its subgroup $L=O(k\infty,Z_p)$, and the subgroup $K=O(\infty,Z_p)$ embedded to $L$…

In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincar\'e-Hopf type formulae which relates the…

Foa a given local ring, we study the fiber cone of ideals with analytic spread one. In this case, the fiber cone has a strucure as a module over its Noether normalization which is a polynomial ring in one variable over the residue field.…

According to a program of Braverman, Kazhdan and Ng\^o Bao Ch\^au, for a large class of split unramified reductive groups $G$ and representations $\rho$ of the dual group $\hat{G}$, the unramified local $L$-factor $L(s,\pi,\rho)$ can be…

We introduce and analyse a general notion of fundamental group for noncommutative spaces, described by differential graded algebras. For this we consider connections on finitely generated projective bimodules over differential graded…

We study the structure constants of the class algebra $R_Z(G_n)$ of the wreath products $G_n$ associated to an arbitrary finite group G with respect to the basis of conjugacy classes. We show that a suitable filtration on $R_Z(G_n)$ gives…

This work introduces author's theory of Bruhat-Tits buildings over higher dimensional local fields. The theory is illustrated with the buildings for PGL(2) and PGL(3) for one- and two-dimensional local fields.

Let $L/\mathbb{Q}_p$ be a finite extension. We introduce $L$-typical prisms, a mild generalization of prisms. Following ideas of Bhatt, Scholze, and Wu, we show that certain vector bundles, called Laurent $F$-crystals, on the $L$-typical…

We outline a general procedure that builds classifying spaces for generalized Thompson groups $\Gamma$. The construction depends on a small number of choices: (1) an inverse semigroup $S$ of partial transformations that ``locally determine"…

Given a finite cocommutative Hopf algebra $A$ over a commutative regular ring $R$, the lattice of localising tensor ideals of the stable category of Gorenstein projective $A$-modules is described in terms of the corresponding lattices for…