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SUMMARY:Polarizations and torsors of abelian varieties - Jef Laga\, Cambri
 dge/St John's College
DTSTART:20251029T141500Z
DTEND:20251029T151500Z
UID:TALK238249@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Polarizations on abelian varieties are a central part of their
  theory\, for example when constructing moduli spaces. Over an algebraical
 ly closed field\, every polarization is represented by an ample line bundl
 e on A\, but this need not be true in general. To remedy this\, Poonen and
  Stoll have asked: can every polarization be represented by a line bundle 
 on some torsor under A? This question also arises naturally from the work 
 of Alexeev on compactifying moduli of abelian varieties. In this talk\, we
  will explain why the answer to this question is often yes and sometimes n
 o. Along the way\, we will encounter Mumford theta groups\, negligible gro
 up cohomology and twisted cohomology of moduli spaces of abelian varieties
 .
LOCATION:CMS MR13
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