Logic Seminar: A clear view through descent and residual domination in valued fields, by Mariana Vicaria
December 2, 2025
3:00 PM - 3:50 PM
Mariana Vicaria (University of Chicago): A clear view through descent and residual domination in valued fields
In this talk, first I will present a very simplified proof of descent for stably dominated types in ACVF. I will also state a more general version of descent for stably dominated types in any theory, dropping the hypothesis of the existence of invariant extensions. This first part is work with Pierre Simon.
Later I will present a whole theory of residual domination for henselian valued fields of equicharacteristic zero. This is joint work with Pablo Cubides and Silvain Rideau Kikuchi. Among other things, we applied the original descent to prove a change of base statement for residual domination. We also show that in any henselian valued field (over an algebraically closed base), a global invariant type is residually dominated if and only if it is orthogonal to the value group, if and only if its reduct in ACVF is stably dominated. The results extend to valued fields with operators.
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Date posted
Dec 5, 2025
Date updated
Dec 5, 2025
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