We give a description of endomorphism rings of Weil restrictions of abelian varieties with respect to finite Galois extensions of fields. The results are applied to study the isogeny decompositions of Weil restrictions. 2000 Mathematics Subject Classification Primary: 14K15, Secondary: 11G10.

We give a new proof that the completion of the Weil-Petersson metric on Teichmüller space is Gromov-hyperbolic if the surface is a five-times punctured sphere or a twice-punctured torus. Our methods make use of the synthetic geometry of the Weil-Petersson metric.

We review the localization formula due to Berline-Vergne and Atiyah-Bott, with applications to the exact stationary phase phenomenon discovered by Duistermaat-Heckman. We explain the Weil model of equivariant cohomology and recall its relation to BRST. We show how to quantize the Weil model, and obtain new localization formulas which, in particular, apply to Hamiltonian spaces with group valued...

We develop a general method for bounding Mordell-Weil ranks of Jacobians of arbitrary curves of the form y = f(x). As an example, we compute the Mordell-Weil ranks over Q and Q( √ −3) for a non-hyperelliptic curve of genus 8.

The story of the Weil conjectures and the development of etale cohomology is the story of one of the great triumphs of 20th century algebraic geometry. The problem treated is exceedingly elementary – counting solutions of polynomials over finite fields – but the proofs require and indeed motivated the creation of an astonishing array of sophisticated technical machinery. The earliest echoes of ...

BACKGROUND Disruption of the plantar plate of the lesser metatarsophalangeal (MTP) joints leads to significant instability. Despite the fact that plantar plate disorders are common, the best mode of treatment remains controversial with operative treatments having variable and somewhat unpredictable clinical outcomes. METHODS Lesser MTP joints from the second, third, and fourth toes from fresh...

We generalize the result of [11] on incompressibility of Galois Weil transfer of generalized Severi-Brauer varieties, to direct products of varieties of such type; as shown in [11], this is needed to compute essential dimension of representations of finite groups. We also provide a generalization to non-Galois (separable) Weil transfer.

We give characterizations of contractible curves on proper normal algebraic surfaces in terms of complementary Weil divisors. From this we obtain some generalizations of the classical criteria for contractibility of Castelnuovo and Artin. Furthermore, we will derive a finiteness result on homogeneous spectra defined by Weil divisors on proper normal algebraic surfaces.

A general theory of characteristic classes of quantum principal bundles is sketched, incorporating basic ideas of classical Weil theory into the conceptual framework of non-commutative differential geometry. A purely cohomological interpretation of the Weil homomorphism is given, together with a geometrical interpretation via quantum invariant polynomials. A natural spectral sequence is describ...

We show that the Prym map for 4-th cyclic étale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.