Seminar

Abstract:

We outline a method for reducing diophantine problems over certain infinitely ramified extensions of the p-adic numbers to their characteristic p analogues. More generally, this reduction also applies in the context of first order statements.  The proof uses basic machinery from perfectoid geometry together with an unpublished result by van den Dries.

Motivated by the above reduction, we then report on some work in progress on the characteristic p side. More specifically, motivated by the work of Denef-Schoutens, we address the diophantine problem over Fp[[t]]^{perf} assuming resolution of singularities in positive characteristic.  

Diophantine Problems Over Infinitely Ramified Fields