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SUMMARY:SAG: On the Euler characteristic of ordinary irregular varieties [
 Lecture]
DTSTART:20251211T093000Z
DTEND:20251211T113000Z
DTSTAMP:20260314T230200Z
UID:indico-event-988@math-events.uni-bonn.de
DESCRIPTION:Speakers: Jefferson Baudin\n\nOver the complex numbers\, a use
 ful tool to study the geometry of irregular varieties is generic vanishing
 . This has led to several remarkable results: characterization of abelian 
 varieties by only fixing a few invariants\, deeper understanding of the Eu
 ler characteristic of irregular varieties\, study of their pluricanonical 
 systems\, and so on.\nThese theorems rely on vanishing results of analytic
  nature\, making this whole topic harder to reach in positive characterist
 ic. Our goal in this talk will be to explain how generic vanishing works i
 n positive characteristic\, through the prism of the study of Euler charac
 teristics. We will present the following theorem: if X is a smooth project
 ive ordinary variety of maximal Albanese dimension (i.e. dim(alb(X)) = dim
 (X))\, then the Euler characteristic of the sheaf of top forms is non-nega
 tive. If in addition this quantity is zero\, then the Albanese image of X 
 is fibered by abelian varieties.\nThe proof uses the positive characterist
 ic generic vanishing theory developed by Hacon-Patakfalvi\, as well as our
  recent Witt vector version of Grauert-Riemenschneider vanishing.\n\nhttps
 ://math-events.uni-bonn.de/event/988/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/988/
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