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TZID:Europe/Paris
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TZOFFSETFROM:+0100
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DTSTART:20220327T010000
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DTSTART:20221030T010000
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DTSTART;TZID=Europe/Paris:20220510T160000
DTEND;TZID=Europe/Paris:20220510T173000
DTSTAMP:20260405T203356
CREATED:20220502T091359Z
LAST-MODIFIED:20220502T115516Z
UID:15549-1652198400-1652203800@www.math.ens.psl.eu
SUMMARY:Existential theories of henselian fields\, parameters welcome
DESCRIPTION:The first-order theories of local fields of positive characteristic\, i.e. fields of Laurent series over finite fields\, are far less well understood than their characteristic zero analogues: the fields of real\, complex and p-adic numbers. On the other hand\, the existential theory of an equicharacteristic henselian valued field in the language of valued fields is controlled by the existential theory of its residue field. One is decidable if and only if the other is decidable. When we add a parameter to the language\, things get more complicated. Denef and Schoutens gave an algorithm\, assuming resolution of singularities\, to decide the existential theory of rings like Fp[[t]]\, with the parameter t in the language. I will discuss their algorithm and present a new result (from ongoing work\, with Dittmann and Fehm) that weakens the hypothesis to a form of local uniformization\, and which works in greater generality.
URL:https://www.math.ens.psl.eu/evenement/tba-12/
LOCATION:Sophie Germain salle 1016
CATEGORIES:Théorie des Modèles et Groupes
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