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
The rank of étale cohomology of varieties over -adic or number fields
The rationality of the Poincaré series associated to the p-adic points on a variety.
The reciprocity obstruction for rational points on compactifications of torsors under tori over fields with global duality.
The reduction of a double covering of a Mumford curve.
The Riemann-Roch theorem and geometry, 1854-1914.
The Schottky-Jung theorem for Mumford curves
The Schottky-Jung proportionality theorem, from which the Schottky relation for theta functions follows, is proved for Mumford curves, i.e. curves defined over a non-archimedean valued field which are parameterized by a Schottky group.
The Shafarevich-Tate Conjecture for Pencils of Elliptic Curves on K3 Surfaces.
The sign of the functional equation of the L-function of an orthogonal motive.
The size function h° for a pure cubic field
The solubility of diagonal cubic surfaces
The Strong Lefschetz Principle in Algebraic Geometry.
The structure of proper rigid groups.
The tame fundamental group of an abelian variety and integral points
The Tate conjecture for ordinary K3 surfaces over finite fields.
The topology of rational points.
The two faces of the twisted Kummer surface