BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Zinovy Reichstein (University of British Columbia (Canada)) DTSTART:20210312T171000Z DTEND:20210312T175500Z DTSTAMP:20260423T004658Z UID:FGV/12 DESCRIPTION:Title: Fie lds of definition for linear representations\nby Zinovy Reichstein (Un iversity of British Columbia (Canada)) as part of Finite Groups in Valenci a\n\n\nAbstract\nA classical theorem of Richard Brauer asserts that every finite-dimensional non-modular representation $\\rho$ of a finite group $G $ defined over a field $K$\, whose character takes values in $k$\, descend s to $k$\, provided that $k$ has suitable roots of unity. If $k$ does not contain these roots of unity\, it is natural to ask how far $\\rho$ is fro m being definable over $k$. The classical answer to this question is given by the Schur index of $\\rho$\, which is the smallest degree of a finite field extension $l/k$ such that $\\rho$ can be defined over $l$. In this t alk\, based on joint work with Nikita Karpenko\, Julia Pevtsova and Dave B enson\, I will discuss another invariant\, the essential dimension of $\\r ho$\, which measures ''how far'' $\\rho$ is from being definable over $k$ in a different way by using transcendental\, rather than algebraic field e xtensions. I will also talk about recent results of Federico Scavia on ess ential dimension of representations of algebras.\n LOCATION:https://researchseminars.org/talk/FGV/12/ END:VEVENT END:VCALENDAR