Classification of imaginaries in existentially closed valued difference fields

by Prof. Martin Hils (WWU Münster)

Friday 11 Mar 2022, 11:00 → 12:00 Europe/Rome

Sala Riunioni (Dipartimento di Matematica)

In their seminal work, Haskell, Hrushovski and Macpherson gave a classification of imaginaries (i.e. quotient objects in the definable category) in an algebraically closed valued field K by the so-called geometric sorts, namely the valued field sort together with sorts for all O_K-lattices in K^n and for the reducts of these lattices modulo the maximal ideal of the valuation ring O_K.

In the talk, I will present recent work, joint with Silvain Rideau-Kikuchi, establishing that the geometric sorts are also sufficient to classify the imaginaries in certain existentially closed valued difference fields of residue characteristic 0, in particular in the isometric case, where the automorphism induces the identity on the value group, and in the omega-increasing case, which corresponds to the non-standard  Frobenius automorphism acting on an algebraically closed valued field.