Related papers: The Euler characteristic of $\ell$-adic local syst…

We are interested in the intersection cohomology of the minimal compactification of Siegel modular varieties at some places of bad reduction. We compute the semi-simple trace of the Frobenius morphism on the fibers of the nearby cycles of…

We give the values of the Siegel-Veech constants associated with saddle connections having distinct endpoints on translation surfaces in Prym eigenform loci in $\Omega \mathcal{M}_3(2,2)^{\rm odd}$. In particular, we show that these…

We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative ones, up to certain weights.From these, we obtain some…

In this article, we prove (many parts of) the rank two case of the Kato's local epsilon-conjecture using the Colmez's p-adic local Langlands correspondence for GL_2(Q_p). We show that a Colmez's pairing defined in his study of locally…

We propose two new approaches to the Tannakian Galois groups of holonomic D-modules on abelian varieties. The first is an interpretation in terms of principal bundles given by the Fourier-Mukai transform, which shows that they are almost…

Using a description of the cohomology of local systems on the moduli space of abelian surfaces with a full level two structure, together with a computation of Euler characteristics we find the isotypical decomposition, under the symmetric…

We calculate the orbifold Euler characteristics of all the degree d fine universal compactified Jacobians (defined by Pagani and Tommasi) over the moduli space of stable curves of genus g with n marked points. We show that this orbifold…

We extend results of Kass--Wickelgren to define an Euler class for a non-orientable (or non-relatively orientable) vector bundle on a smooth scheme, valued in the Grothendieck--Witt group of the ground field. We use a root stack…

Let $\rho_\ell$ be a semisimple $\ell$-adic representation of a number field $K$ that is unramified almost everywhere. We introduce a new notion called weak abelian direct summands of $\rho_\ell$ and completely characterize them, for…

In this paper, we compare two different constructions of $p$-adic $L$-functions for modular forms and their relationship to Galois cohomology: one using Kato's Euler system and the other using Emerton's $p$-adically completed cohomology of…

We consider the problem of explicitly computing dimensions of spaces of automorphic or modular forms in level one, for a split classical group $\mathbf{G}$ over $\mathbb{Q}$ such that $\mathbf{G}(\R)$ has discrete series. Our main…

We prove local-global compatibility results at $\ell=p$ for the torsion automorphic Galois representations constructed by Scholze, generalising the work of Caraiani--Newton. In particular, we verify, up to a nilpotent ideal, the…

In our earlier work with Christopher Skinner (J. Eur. Math. Soc 24 (2022), no. 2; DOI 10.4171/JEMS/1124; Arxiv 1706.00201), we constructed Euler systems for the 4-dimensional spin Galois representations corresponding to automorphic forms…

This is a part of our joint program. The purpose of this paper is to study smooth toroidal compactifications of Siegel varieties and their applications, we also try to understand the K\"ahler-Einstein metrics on Siegel varieties through the…

We use the non-proper Morse theory of Palais-Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties, and that of their infinite cyclic covers. As main applications, we obtain the finite generation…

Given a number field we construct a canonical Galois gerbe over it and show that its cohomology provides a bridge between the refined local endoscopy introduced in arXiv:1304.3292 and classical global endoscopy. As particular applications,…

In this paper, we associate Galois representations to globally generic cuspidal automorphic representations on GSp(4), over a totally real field F, which are Steinberg at some finite place. This association is compatible with the local…

We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single double zero. These curves can all be embedded in Hilbert…

The l-adic parabolic cohomology groups attached to noncongruence subgroups of SL_2(Z) are finite-dimensional representations of Gal(Qbar/F) for some number field F. We exhibit examples (with F=Q) giving rise to Galois representations whose…

We prove that the reduction mod \ell of the local Langlands correspondence between supercuspidal representations of GL_n(F), where F is a finite extension of Q_p, and representations of the Galois group of F is well-defined. The results and…