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Seminar

DDC - Junior Seminar: Diophantine problems over infinitely ramified fields December 01, 2020 (09:00 AM PST - 10:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Konstantinos Kartas (University of Oxford)
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Diophantine Problems Over Infinitely Ramified Fields

Abstract/Media

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  The proof uses basic machinery from perfectoid geometry together with an unpublished result by van den Dries.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.  

 

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Diophantine Problems Over Infinitely Ramified Fields

H.264 Video 25590_29148_8661_Diophantine_Problems_Over_Infinitely_Ramified_Fields.mp4