We extend a theorem of Masur and Wolf which says that given a hyperbolic surface S, every isometry of the Teichmüller space for S with the Weil–Petersson metric is induced by an element of the mapping class group for S. Our argument handles the previously untreated cases of the four-holed sphere and the torus with one or two holes.

An explicit expression for the ε-factor εK((V,N),ψ,dμ) of a representation (V,N) of the Weil-Deligne group WDK of a local field K is given in terms of the nonabelian local class field theory of K.

We show that inclusion order and single-step inclusion coincide for higher 1 Preliminaries Higher Bruhat orders were introduced by Manin and Schechtman 5] as generalizations of the weak Bruhat order on the symmetric group S n. Further investigations of the subject are Voevodskij and Kapranov 6], Ziegler 7], Edelman and Reiner 1, 2] and Felsner and Weil 3]. Let us review the deenition.

We prove that the triviality of the Galois action on the suitably twisted odd-dimensional étale cohomogy group with finite coefficients of an absolutely irreducible smooth projective variety implies the existence of certain primitive roots of unity in the field of definition of the variety. This text was inspired by an exercise in Serre’s Lectures on the Mordell–Weil theorem.

We shall show that the Picard number of the generic fiber of an abelian fibered hyperkähler manifold over the projective space is always one. We then give a few applications for the Mordell-Weil group. In particular, by deforming O’Grady’s 10dimensional manifold, we construct an abelian fibered hyperkähler manifold of MordellWeil rank 20, which is the maximum possible among all known ones.

In this paper, we construct a point on the Jacobian of a non-hyperelliptic genus four curve which is defined over a quadratic extension of the base field. We then show that this point generates the Mordell–Weil group of the Jacobian of the universal genus four curve.

We give a construction of Connes-Moscovici’s cyclic cohomology for any Hopf algebra equipped with a character. Furthermore, we introduce a non-commutative Weil complex, which connects the work of Gelfand and Smirnov with cyclic cohomology. We show how the Weil complex arises naturally when looking at Hopf algebra actions and invariant higher traces, to give a non-commutative version of the usua...

By showing that the elliptic curve (x2 13)(y2 13) = 48 has infinitely many rational points, we prove that Letac's construction produces infinitely many genuinely different ideal 9th-order multigrades. We give one (not very small) new example, and, by finding the Mordell-Weil group of the curve, show how to find all examples obtainable by Letac's method.

A finite oscillator system was introduced by Gurevich, Hadani and Sochen. This is a survey of how the system is constructed using Weil representation on the group SL(2,Fp) and its applications on discrete radar and CDMA system. Finally, explicit algorithms for computing the finite split and non-split oscillator systems S and S are described.

Let V be a de-Rham representation of the Galois group of a local field of mixed characteristic (0, p). We relate the Swan conductor of the associated Weil-Deligne representation to the irregularity of the corresponding p-adic differential equation. 2000 Mathematics Subject Classification: 11F80,11F85,11S15,12H25