BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Peter Wear (University of Utah) DTSTART:20230411T210000Z DTEND:20230411T220000Z DTSTAMP:20260423T024754Z UID:UAANTS/67 DESCRIPTION:Title: The conjugate uniformization via 1-motives\nby Peter Wear (University of Utah) as part of University of Arizona Algebra and Number Theory Semina r\n\nLecture held in ENR2 S395.\n\nAbstract\nGiven an abelian variety $A$ over a finite extension $K$ of $\\mathbb{Q}_p$\, Fontaine constructed an i ntegration map from the Tate module of A to its Lie algebra. This map give s the splitting of the Hodge-Tate short exact sequence. Recent work of Iov ita-Morrow-Zaharescu extends this integration map to the $\\overline{K}$ p oints of the perfectoid universal cover of $A$. They used this result to g ive a uniformization of the $\\mathcal{O}_{\\overline K}$ points of the un derlying $p$-divisible group. In this talk\, we explain joint work with Se an Howe and Jackson Morrow in which we give a different perspective on thi s uniformization using 1-motives. We will first give some intuition from t he complex uniformization of semi-abelian varieties and some background an d motivation on $p$-divisible groups. Then we will explain how to construc t the $p$-divisible group of a 1-motive and how this gives the desired uni formization. Finally\, we will point out some interesting geometric featur es of this map: it embeds the rigid analytic points of a $p$-divisible gro up into an etale cover of a negative Banach-Colmez space.\n LOCATION:https://researchseminars.org/talk/UAANTS/67/ END:VEVENT END:VCALENDAR