271 citations · 561 across the 18 of their papers we have counts for
19 papers
Geometric proofs of theorems of Ax-Kochen and Ersov
Jan Denef
We give an algebraic geometric proof of the Theorem of Ax and Kochen on p-adic diophantine equations in many variables. Unlike Ax-Kochen's proof, ours does not use any notions from…
Some remarks on toroidal morphisms
Jan Denef
This note contains some results related to the definitions of toroidal embeddings and toroidal morphisms over non-closed fields of characteristic zero.
Monomialization of morphisms and p-adic quantifier elimination
Jan Denef
We give a short proof of Macintyre's Theorem on Quantifier Elimination for the p-adic numbers, using a version of monomialization that follows directly from the Weak Toroidalizatio…
Proof of a conjecture of Colliot-Thélène
Jan Denef
We prove a conjecture of Colliot-Thélène that implies the Ax-Kochen Theorem on p-adic forms. We obtain it as an easy consequence of a diophantine excision theorem whose proof forms…
Weak toroidalization over non-closed fields
Dan Abramovich, Jan Denef, Kalle Karu
We prove that any dominant morphism of algebraic varieties over a field k of characteristic zero can be transformed into a toroidal (hence monomial) morphism by projective biration…
Orbital integrals for linear groups
R. Cluckers, J. Denef
For a linear group acting on an absolutely irreducible variety over the rationals $\QQ$, we describe the orbits of $X(\QQ_p)$ under $G(\QQ_p)$ and of $X(\FF_p((t)))$ under…