A note on Enriques' surfaces in characteristic 2
Diophantine approximation and deformation
Double fibres and double covers: paucity of rational points
Factoring polynomials in finite fields: an application of Lang-Weil to a problem in graph theory.
Klassifikationstheorie algebraischer Varietäten der Dimension drei
La loi de réciprocité de Shimura pour les fonctions de Jacobi
l-adic Lefschetz numbers of arithmetic schemes.
Local-global principle for certain biquadratic normic bundles
Let X be a proper smooth variety having an affine open subset defined by the normic equation over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel’s hypothesis.
On the de Rham-Witt complex attached to a semi-stable family
On the Kodaira Dimension of the Moduli Space of Curves.
Orbifolds, special varieties and classification theory
This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...
Orbifolds, special varieties and classification theory: an appendix
For any compact Kähler manifold and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in , the existence of a meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of given in the previous paper of this fascicule, as well as in many other questions.
-adic cycles
Quartic del Pezzo surfaces over function fields of curves
We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to the fibration, and mappings to the intermediate Jacobian of the total space. We exhibit examples where these are birational, which has applications to arithmetic questions, especially over finite fields.
Shimuras Reziprozitätsgesetz für den Körper der arithmetischen elliptischen Funktionen beliebiger Stufe.
The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
The Hyperelliptic Locus with Special Reference to Characteristic Two.
Коммутативные формальные группы