Related papers: Arithmetic models for Shimura varieties

We define and study new filtrations called of stratification of a perverse sheaf on a scheme; beside the cases of the weight or monodromy filtrations, these filtrations are available whatever are the ring of coefficients. We illustrate…

We study the motivic cohomology of the special fiber of quaternionic Shimura varieties at a prime of good reduction. We exhibit classes in these motivic cohomology groups and use this to give an explicit geometric realization of level…

Estimates of some integrals related to variations of smooth functions are presented.

Polynomial system solving has seen major progress in both theory and practice over the past decade. A landmark achievement was addressing Smale's 17th problem, establishing average-case polynomial-time algorithms for computing approximate…

We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.

This paper presents the status of the APEmille project, which is essentially completed, as far as machine development and construction is concerned. Several large installations of APEmille are in use for physics production runs leading to…

We prove the Mumford-Tate conjecture for those abelian varieties over number fields, whose simple factors of their adjoint Mumford-Tate groups have over $\dbR$ certain (products of) non-compact factors. In particular, we prove this…

We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.

We propose a conjectural theory of $p$-integral models of Shimura varieties with level structure at $p$ given by a class of normal subgroups of parahoric subgroups with abelian quotient group. The role of the theory of local models is…

We give a modern introduction to the moduli of sheaves. After reviewing the classical theory, we give a catalogue of results from the last decade. We then consider a more "symmetric" formulation of the theory by working with gerbes from the…

We retrace the recent history of the Umbral Calculus. After studying the classic results concerning polynomial sequences of binomial type, we generalize to a certain type of logarithmic series. Finally, we demonstrate numerous typical…

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…

This, fourth paper of the series (see previous papers in Refs.[1-3]) derives approximate equations for future numerical studies of initial evolution of hurricanes, develops new analytical models of hurricane genesis and maturing, and…

Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are…

We study Shimura (special) subvarieties in the moduli space $A_{p,D}$ of complex abelian varieties of dimension $p$ and polarization type $D$. These subvarieties arise from families of covers compatible with a fixed group action on the base…

We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.

A conjecture by Yves Andre and Frans Oort says that closed subvarieties of Shimura varieties that contain a Zariski dense subset of special points are subvarieties of Hodge type. We prove this in the case where the subvariety is a curve…

Work in progress concerning alternative formalizations of arithmetic.

In this paper we prove the equidistribution of bounded sequences of special subvarieties in a general mixed Shimura varieties, a notion adapted from the pure case treated by Clozel, Ullmo, and Yafaev in the study of the Andre-Oort…

We study improved variants of L\"uscher's algorithm, including the cases of staggered fermions and finite density.