Related papers: D\'ecomposition au-dessus des param\`etres de Lang…

We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge…

Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by Moeglin and for the exceptional Chevalley group G_2 by…

We compute the cohomology with compact supports of a Picard modular surface as a virtual module over the product of the appropriate Galois group and the appropriate Hecke algebra. We use the method developed by Ihara, Langlands, and…

Let $F$ be a totally real number field. We prove that a character of the spherical Hecke algebra appearing in the completed cohomology of Hilbert modular varieties is modular if the associated Galois representation is absolutely…

We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex…

We review the analog of Fontaine's theory of crystalline $p$-adic Galois representations and their classification by weakly admissible filtered isocrystals in the arithmetic of function fields over a finite field. There crystalline Galois…

The cuspidal cohomology groups of arithmetic groups in certain infinite dimensional Modules are computed. As a result we get a simultaneous generalization of the Patterson-Conjecture and the Lewis-Correspondence.

Linear categories naturally have several identification relations : isomorphisms, categorical equivalences and Morita equivalences. In this thesis, we construct the classifying stacks for these three relations ($\ukcatiso$, $\ukcateq$,…

Let $K$ be a field of characteristic two, and let $\lambda$ be a two-part partition of some natural number $r$. Denote the permutation module corresponding to the (maximal) Young subgroup $\Sigma_\lambda$ in $\Sigma_r$ by $M^\lambda$. We…

The purpose of this paper is extend the notion of morphism of groupoids introduced by Zakrzewski to locally compact $\sigma$-compact groupoids endowed with Haar systems and to use the extension to construct a covariant functor from this…

We study the geometry and cohomology of the (generic fibres) of formal deformation schemes of one-dimensional formal modules of finite height. By the work of Boyer (in mixed characterististic) and Harris and Taylor, the l-adic etale…

Our main theorem describes the degree 0 cohomology of Igusa varieties in terms of one-dimensional automorphic representations in the setup of mod p Hodge-type Shimura varieties with hyperspecial level at p, mirroring the well known analogue…

We introduce Hochschild (co-)homology of morphisms of schemes or analytic spaces and study its fundamental properties. In analogy with the cotangent complex we introduce the so called (derived) Hochschild complex of a morphism; the…

We find a natural $L_{\omega_1,\omega}$-axiomatisation $\Sigma$ of a structure on the upper half-plane $\mathbb{H}$ as the covering space of modular curves. The main theorem states that $\Sigma$ has a unique model in every uncountable…

We study the moduli spaces which classify smooth surfaces along with a complex line bundle. There are homological stability and Madsen--Weiss type results for these spaces (mostly due to Cohen and Madsen), and we discuss the cohomological…

In this short note, we compute the Betti numbers of the moduli stack of flat SU(3)-bundles over a Klein bottle. We also handle the general compact group case over RP^2. In all cases the cohomology is found to be equivariantly formal,…

We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the r-th central derivative of non-singular Fourier coefficients of a normalized Siegel--Eisenstein series, and (2) the degree of special…

This paper continues the study of holomorphic semistable principal G-bundles over an elliptic curve. In this paper, the moduli space of all such bundles is constructed by considering deformations of a minimally unstable G-bundle. The set of…

We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of…

In this paper we classify isogeny classes of global $\mathsf{G}$-shtukas over a smooth projective curve $C/\mathbb{F}_q$ (or equivalently $\sigma$-conjugacy classes in $\mathsf{G}(\mathsf{F} \otimes_{\mathbb{F}_q} \overline{\mathbb{F}_q})$…