Martin Hils: Classification of imaginaries in valued fields with automorphism
Thursday, 14.05.2020 11:00 im Raum via Zoom
The imaginaries in the theory ACVF of non-trivially 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.
Angelegt am Monday, 04.05.2020 09:23 von Martina Pfeifer
Geändert am Monday, 04.05.2020 09:28 von Martina Pfeifer
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