Logic Seminar - Martin Hils

Tue, 25/02/202014:00-16:00
Ross building - Room 63,
Martin Hils will speal about Classification of imaginaries in valued fields with automorphism.

Title: Classification of imaginaries in valued fields with automorphism

Abstract: The imaginaries in the theory ACVF of non-triviallally valued algebraically closed
valued fields are classified by the so-called 'geometric' sorts. This is a fundamental
result due to Haskell-Hrushovski-Macpherson. We show that the imaginaries in
henselian equicharacteristic 0 valued fields may be reduced, under rather general
assumptions, to the geometric sorts and to imaginaries in RV together with sorts
for certain finite-dimensional vector spaces over the residue field.

In the talk, I will mainly speak about an application of this reduction, which has been
the initial motivation of our work: The imaginaries in the theory VFA of algebraically
closed non-trivially valued fields of equicharacteristic 0, endowed with a non-standard
Frobenius automorphism, are classified by the geometric sorts. This requires an
understanding of imaginaries in pure short exact sequences, and a key result from
Hrushovski's groupoids paper.