Related papers: Trace formula for component groups of N\'eron mode…

It is known that the etale cohomology of a potentially good abelian variety over a local field K is determined by its Euler factors over the extensions of K. We extend this to all abelian varieties, show that it is enough to take extensions…

We introduce the N\'eron component series of an abelian variety $A$ over a complete discretely valued field. This is a power series in $\Z[[T]]$, which measures the behaviour of the number of components of the N\'eron model of $A$ under…

We consider Tate cycles on an Abelian variety $A$ defined over a sufficiently large number field $K$ and having complex multiplication. We show that there is an effective bound $C = C(A,K)$ so that to check whether a given cohomology class…

Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\mathrm{GL}_2$ along…

We establish a trace formula for rigid varieties $X$ over a complete discretely valued field, which relates the set of unramified points on $X$ to the Galois action on its \'etale cohomology. We develop a theory of motivic integration for…

We express the Frobenius-Hecke traces on the compactly supported cohomology of a Shimura variety of abelian type in terms of elliptic parts of stable Arthur-Selberg trace formulas for the endoscopic groups. This confirms predictions of…

Let $U$ be a smooth affine curve over a number field $K$ with a compactification $X$ and let $\mathbb L$ be a rank $2$, geometrically irreducible $\bar{\mathbb Q}_\ell$-local system on $U$ with cyclotomic determinant that extends to an…

We give complete descriptions of the tracial states on both the universal and reduced crossed products of a C*-dynamical system consisting of a unital C*-algebra and a discrete group. In particular, we also answer the question of when the…

Let $X$ be a smooth curve defined over the fraction field $K$ of a complete d.v.r. $R$, and let $K'/K$ be a tame extension. We study extensions of the $G = \Gal(K'/K)$-action on $ X_{K'} $ to certain regular models of $X_{K'}$ over $R'$,…

We establish the invariant trace formula (\`a la Arthur) for the ad\'elic covers of connected reductive groups over a number field, under the hypothesis that the trace Paley-Wiener theorem is verified for all Levi subgroups at the real…

We present an explicit expression of the cohomology complex of a constructible sheaf of abelian groups on the small \'etale site of an irreducible curve over an algebraically closed field, when the torsion of the sheaf is invertible in the…

Let $A$ be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the N\'eron model of $A$ that measures the behaviour of the N\'eron model under tame base change. We interpret the…

In our previous study of duality for complete discrete valuation fields with perfect residue field, we treated coefficients in finite flat group schemes. In this paper, we treat abelian varieties. This in particular implies Grothendieck's…

Motivated by traces of matrices and Euler characteristics of topological spaces, we expect abstract traces in a symmetric monoidal category to be "additive". When the category is "stable" in some sense, additivity along cofiber sequences is…

We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group is compact. Two interesting examples of the quotient…

We make connections of a counting problem of Eulerian cycles for undirected graphs to homological spectral graph theory, and formulate explicitly a trace formula that identifies the number of Eulerian circuits on an Eulerian graph with the…

We make further observations on the features of Galois cohomology in the general model theoretic context. We make explicit the connection between forms of definable groups and first cohomology sets with coefficients in a suitable…

Let $p$ be a prime, let $K$ be a discretely valued extension of $\mathbb{Q}_p$, and let $A_{K}$ be an abelian $K$-variety with semistable reduction. Extending work by Kim and Marshall from the case where $p>2$ and $K/\mathbb{Q}_p$ is…

We study the motivic Serre invariant of a smoothly bounded algebraic or rigid variety $X$ over a complete discretely valued field $K$ with perfect residue field $k$. If $K$ has characteristic zero, we extend the definition to arbitrary…

We describe an approach to express the geometric side of the Arthur-Selberg trace formula in terms of zeta integrals attached to prehomogeneous vector spaces. This will provide explicit formulas for weighted orbital integrals and for the…