The local monodromy as a generalized algebraic correspondence (with an appendix by Spencer Bloch).
The "main conjectures" of Iwasawa theory for imaginary quadratic fields.
The meromorphic continuation of a zeta function of Weil and Igusa Type.
The Modell-Weil groups of unirational quasi-elliptic surfaces in characteristic 3.
The modified diagonal cycle on the triple product of a pointed curve
Let be a curve over a field with a rational point . We define a canonical cycle . Suppose that is a number field and that has semi-stable reduction over the integers of with fiber components non-singular. We construct a regular model of and show that the height pairing is well defined where and are correspondences. The paper ends with a brief discussion of heights and -functions in the case that is a modular curve.
The modularity of the Barth-Nieto quintic and its relatives.
The moduli spaces of polarized abelian varieties.
The Mordell conjecture revisited
The non rationality of the generic Enriques' threefold
The number of points on certain families of hypersurfaces over finite fields
The overconvergence of morphisms of etale -spaces on a local field
The -adic finite Fourier transform and theta functions.
The -part of Tate-Shafarevich groups of elliptic curves can be arbitrarily large
In this paper we show that for every prime the dimension of the -torsion in the Tate-Shafarevich group of can be arbitrarily large, where is an elliptic curve defined over a number field , with bounded by a constant depending only on . From this we deduce that the dimension of the -torsion in the Tate-Shafarevich group of can be arbitrarily large, where is an abelian variety, with bounded by a constant depending only on .
The periods of abelian varieties with complex multiplication and the spectral values of certain zeta functions
The Picard group of Siegel modular threefolds.
The polynomial and elliptic curves of conductor 11
The p-Rank of Artin-Schreier Curves.
The primitive conjugacy classes and the generalized homology group of a finite graph
The probability that a complete intersection is smooth
Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension. This generalizes the case of a single hypersurface, due to Poonen. We use this result to give a probabilistic model for the number of rational points of such a complete intersection. A somewhat surprising corollary is that the number of rational points on a random smooth intersection...
The product of linear forms in a field of series and the Riemann hypothesis for curves