This is the second of our two papers on the Siegel-Weil theorem for loop groups. In the first paper [3] we proved the Siegel-Weil theorem for (finite dimensional) snt-modules ([3], Theorem 8.1). In the present paper we use this result to obtain the Siegel-Weil theorem for loop groups, Theorem 7.5, below. In addition to the corresponding result for snt-modules, our proof depends on a convergence...

We establish various properties of the definition of cohomology of topological groups given by Grothendieck, Artin and Verdier in SGA4, including a Hochschild-Serre spectral sequence and a continuity theorem for compact groups. We use these properties to compute the cohomology of the Weil group of a totally imaginary field, and of the Weil-étale topology of a number ring recently introduced by ...

Let K be a number field and A an abelian variety over K. The K-rational points of A are known to constitute a finitely generated abelian group (Mordell-Weil theorem). The problem studied in this paper is to find an explicit upper bound for the rank r of its free part in terms of other invariants of A/K. This is achieved by a close inspection of the classical proof of the so-called ‘weak Mordell...

— By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space. Using a modification of the classical local Langlands correspondence, we associate with any pair consisting of a Weil-Deligne group representation and a type ...

In this note we extend the computations described in [4] by computing the analytic order of the Tate-Shafarevich group III for all the curves in each isogeny class; in [4] we considered the strong Weil curve only. While no new methods are involved here, the results have some interesting features suggesting ways in which strong Weil curves may be distinguished from other curves in their isogeny ...

Let T (S) be the Teichmüller space of an oriented surface S of finite type. We discuss the action of subgroups of the mapping class group of S on the CAT(0)-boundary of the completion of T (S) with respect to the Weil-Petersson metric. We show that the set of invariant Borel probability measures for the Weil-Petersson flow on moduli space which are supported on a closed orbit is dense in the sp...

The Weil-Felix reaction helps in the diagnosis of the majority of cases of typhus group of fevers, but it sometimes does not help to differentiate between them, e.g. both epidemic and murine typhus fever produce agglutinins against Proteus 0X19 and to a lesser titre against 0X2 in the sera of patients, and from a Weil-Felix test alone it is not possible to say if one is dealing with a case of m...

Our main result is that the Weil representation of the symplectic group Sp(2n, F ), where F is a non-archimedian local field of residue characteristic 6= 2, can be realized over a number field K. We take an infinite-dimensional complex vector space V such that the Weil representation is given by ρ : Sp(2n, F ) → PGL(V) and we find a K-subspace V0 of V such that ρ(g)(V0) = V0 for all g ∈ Sp(2n, ...