Speaker:
Konstantinos Kartas (currently Universität Münster)

Title:
Diophantine problems over tamely ramified fields

Abstract: 
Assuming a certain form of resolution of singularities, we present 
a general existential Ax-Kochen/Ershov principle for tamely ramified 
fields in all characteristics. This specializes to well-known results 
in residue characteristic 0 and unramified mixed characteristic. It 
also encompasses the conditional existential decidability results known 
for Fp((t)) and its finite extensions, due to Denef-Schoutens. On the 
other hand, it also applies to the setting of infinite ramification, 
thereby providing us with an abundance of existentially decidable 
infinitely ramified extensions of Qp and Fp((t)). An application of 
arithmetic interest will be the case of the ramification fields.