Add to ORKGDedicated to the memory of Professor Jun-ichi Igusa Abstract. We give an algebraic geometric proof of the Theorem of Ax and Kochen on p-adic diophantine equations in many vari-ables. Unlike Ax-Kochen’s proof, ours does not use any notions from mathematical logic and is based on weak toroidalization of morphisms. We also show how this geometric approach yields new proofs of the Ax-Kochen-Eršov transfer principle for local fields, and of quantifier elimination theorems of Basarab and Pas. 1
: La théorie géométrique des invariants constitue un domaine central de la géométrie algébrique d'au...
The p-adic numbers were introduced by K. Hensel [1] in connection with number theory. The absolute ...
We develop and utilize p-adic Hodge theory in families in the context of local-global aspects of the...
We prove a conjecture of Colliot-Thélène that implies the Ax-Kochen Theorem on p-adic forms. We obta...
We give a short proof of Macintyre's Theorem on Quantifier Elimination for the p-adic numbers, using...
These are the notes of a course for the summer school Model Theory in Bilbao hosted by the Basque Ce...
Let k be a non-archimedean field: a field that is complete with respect to a specified nontrivial no...
We show that a system of r quadratic forms over a -adic field in at least 4r+1 variables will have a...
We present a tutorial survey of quantifier-elimination and decision procedures in p-adic fields. The...
This thesis gives an account of algebraic and analytic results in the geometric theory of valued fie...
AbstractThe main result of this paper is a transfer theorem which describes the relationship between...
This book lays the foundation for a theory of uniformization of p-adic hyperbolic curves and their m...
In this thesis we present the results of four years of research on some aspects of p-adic geometry. ...
In this lecture we introduce the reader to the proof of the p-adic monodromy theorem linking the p-a...
confirmation of Artin’s Conjecture. Let n, t and d1,..., dt be natural numbers. Then Ax and Kochen s...
: La théorie géométrique des invariants constitue un domaine central de la géométrie algébrique d'au...
The p-adic numbers were introduced by K. Hensel [1] in connection with number theory. The absolute ...
We develop and utilize p-adic Hodge theory in families in the context of local-global aspects of the...
We prove a conjecture of Colliot-Thélène that implies the Ax-Kochen Theorem on p-adic forms. We obta...
We give a short proof of Macintyre's Theorem on Quantifier Elimination for the p-adic numbers, using...
These are the notes of a course for the summer school Model Theory in Bilbao hosted by the Basque Ce...
Let k be a non-archimedean field: a field that is complete with respect to a specified nontrivial no...
We show that a system of r quadratic forms over a -adic field in at least 4r+1 variables will have a...
We present a tutorial survey of quantifier-elimination and decision procedures in p-adic fields. The...
This thesis gives an account of algebraic and analytic results in the geometric theory of valued fie...
AbstractThe main result of this paper is a transfer theorem which describes the relationship between...
This book lays the foundation for a theory of uniformization of p-adic hyperbolic curves and their m...
In this thesis we present the results of four years of research on some aspects of p-adic geometry. ...
In this lecture we introduce the reader to the proof of the p-adic monodromy theorem linking the p-a...
confirmation of Artin’s Conjecture. Let n, t and d1,..., dt be natural numbers. Then Ax and Kochen s...
: La théorie géométrique des invariants constitue un domaine central de la géométrie algébrique d'au...
The p-adic numbers were introduced by K. Hensel [1] in connection with number theory. The absolute ...
We develop and utilize p-adic Hodge theory in families in the context of local-global aspects of the...