相关论文: Spherical varieties and norm relations in Iwasawa …

In this paper, we investigate a general method to establish tame and norm relations for special cycles in Shimura varieties, using unitary cycles in odd orthogonal Shimura varieties as a guiding example.

We produce first examples of p-local height three TAF homology theories. The corresponding one-dimensional formal groups arise as split summands of the formal groups of certain abelian three-folds, the Shimura variety of which can be…

Iwasawa made the fundamental discovery that there is a close connection between the ideal class groups of $\mathbb{Z}_{p}$-extensions of cyclotomic fields and the $p$-adic analogue of Riemann's zeta functions…

A general framework for the reduction of the equations defining classes of spherical varieties to (maybe infinite dimensional) grassmannians is proposed. This is applied to model varieties of type A, B and C; in particular a standard…

The goal of the memoir is to develop a new cohomology theory which encompasses De Rham and Dolbeault cohomology as well as Deligne Beilinson cohomology, in the context of general complex analytic manifolds. The special case of the Iwasawa…

We show that the cohomology of canonical extensions of automorphic vector bundles over toroidal compactifications of Shimura varieties can be computed by relative Lie algebra cohomology of automorphic forms. Our result is inspired by and…

We construct Eigenvarieties for PEL Shimura varieties which interpolate cuspidal, finite slope automorphic forms for PEL Shimura varieties appearing as global sections of (coherent) automorphic sheaves, under the hypothesis that the primes…

Using $l$-adic completed cohomology in the context of Shimura varieties of Kottwitz-Harris-Taylor type attached to some fixed similitude group $G$, we prove, allowing to increase the levet at $l$, some new automorphic congruences between…

Let p>2 be a prime and let X be a compactified PEL Shimura variety of type (A) or (C) such that p is an unramified prime for the PEL datum. Using the geometric approach of Andreatta, Iovita, Pilloni, and Stevens we define the notion of…

We introduce a cohomology theory for a class of projective varieties over a finite field coming from the canonical trace on a C*-algebra attached to the variety. Using the cohomology, we prove the rationality, functional equation and the…

This paper is devoted to a discussion of Gromov-Witten-Welschinger (GWW) classes and their applications. In particular, Horava's definition of quantum cohomology of real algebraic varieties is revisited by using GWW-classes and it is…

The object of this work is to present the status of art of an open problem: to provide an analogue for Shimura curves of the Ihara's lemma \cite{Ihara73} which holds for modular curves. We will describe our direct result towards the…

We prove that the generic part of the mod l cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree, extending our previous work to a non-compact case. The result…

We develop a sheaf cohomology theory of algebraic varieties over an algebraically closed non-trivially valued non-archimedean field $K$ based on Hrushovski-Loeser's stable completion. In parallel, we develop a sheaf cohomology of definable…

Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus…

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…

The Eichler-Shimura isomorphism realizes the automorphic representation generated by an automorphic newform in certain cohomology of an arithmetic group. In this short note, we give a cohomological interpretation of the Eichler-Shimura…

We investigate a novel geometric Iwasawa theory for $\mathbf{Z}_p$-extensions of function fields over a perfect field $k$ of characteristic $p>0$ by replacing the usual study of $p$-torsion in class groups with the study of $p$-torsion…

We study some automorphic cohomology classes of degree one on the Griffiths-Schmid varieties attached to some unitary groups in 3 variables. Using partial compactifications of those varieties, constructed by K. Kato and S. Usui, we define…

We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular p-adic integral models for these varieties over odd primes p at which the level subgroup is the connected…