Poles of Igusa's local zeta function and monodromy
Poles of -adic complex powers and Newton polyhedra
Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group
2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.If F is a polynomial automorphism over a finite field Fq in dimension n, then it induces a permutation pqr(F) of (Fqr)n for every r О N*. We say that F can be “mimicked” by elements of a certain group of automorphisms G if there are gr О G such that pqr(gr) = pqr(F). Derksen’s theorem in characteristic zero states that the tame automorphisms in dimension n і 3 are generated by the affine maps and the one map (x1+x22, x2,ј, xn). We show...
Polynomials with integral coefficients, equivalent to a given polynomial.
Potential theory and Lefschetz theorems for arithmetic surfaces
Power-free values, large deviations, and integer points on irrational curves
Let be a polynomial of degree without roots of multiplicity or . Erdős conjectured that, if satisfies the necessary local conditions, then is free of th powers for infinitely many primes . This is proved here for all with sufficiently high entropy.The proof serves to demonstrate two innovations: a strong repulsion principle for integer points on curves of positive genus, and a number-theoretical analogue of Sanov’s theorem from the theory of large deviations.
Preuve des conjectures de Tate et de Shafarevitch
Prime to fundamental groups and tame Galois actions
We show that for a local, discretely valued field , with residue characteristic , and a variety over , the map to the outer automorphisms of the prime to geometric étale fundamental group of maps the wild inertia onto a finite image. We show that under favourable conditions depends only on the reduction of modulo a power of the maximal ideal of . The proofs make use of the theory of logarithmic schemes.
Primzahlfragen in der Diophantischen Geometrie.
Principe de Boyarsky et ...-modules.
Principe de Hasse et approximation faible sur certaines hypersurfaces
Principe de Hasse pour certaines variétés rationnelles
Problems and results on the distribution of algebraic points on algebraic varieties
This is a survey paper on the distribution of algebraic points on algebraic varieties.
Products of special values of modular L-functions and their applications
Produits dans la cohomologie holomorphe des variétés de Shimura.
Produits dans la cohomologie holomorphe des variétés de Shimura II: Calculs et applications.
Profondeur d’anneaux d’invariants en caractéristique
Prolongement de la valeur absolue de Gauss et problème de Skolem
Prolongement de revêtements galoisiens en géométrie rigide
Prolongements analytiques d’une classe de fonctions zêta des hauteurs et applications
Nous montrons dans la première partie l’existence d’un prolongement méromorphe à tout le plan complexe et explicitons les propriétés et quelques conséquences, d’une large classe de séries zêta des hauteurs associées à l’espace projectif