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SUMMARY:Lang-Weil type bounds in finite difference fields
DTSTART:20240523T123000Z
DTEND:20240523T133000Z
DTSTAMP:20240530T160600Z
UID:indico-event-274@events.dm.unipi.it
DESCRIPTION:Speakers: Martin Hils (Universität Münster)\n\nWe prove Lang
-Weil type bounds for the number of rational points of difference varietie
s over finite difference fields\, in terms of the transformal dimension of
the variety and assuming the existence of a smooth rational point. It fol
lows that in (certain) non-principal ultraproducts of finite difference fi
elds the coarse dimension of a quantifier free type equals its transformal
transcendence degree.The proof uses a strong form of the Lang-Weil estima
tes and\, as key ingredient to obtain equidimensional Frobenius specializa
tions\, the recent work of Dor and Hrushovski on the non-standard Frobeniu
s acting on an algebraically closed non-trivially valued field\, in partic
ular the pure stable embeddedness of the residue difference field in this
context.This is joint work with Ehud Hrushovski\, Jinhe Ye and Tingxiang Z
ou. \n\nhttps://events.dm.unipi.it/event/274/
LOCATION:Aula Riunioni (Dipartimento di Matematica)
URL:https://events.dm.unipi.it/event/274/
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