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SUMMARY:Libby Taylor (Stanford University)
DTSTART:20200914T200000Z
DTEND:20200914T210000Z
DTSTAMP:20260423T052805Z
UID:AGSAGS/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGSAGS/1/">F
 ourier-Mukai theory for stacky genus 1 curves</a>\nby Libby Taylor (Stanfo
 rd University) as part of American Graduate Student Algebraic Geometry Sem
 inar\n\n\nAbstract\nWe will discuss a theory of derived equivalences for c
 ertain Artin stacks.  We will apply this theory to study the derived categ
 ories of genus 1 curves and of their Picard stacks.  Some questions we wil
 l answer: when are two $\\mathbb{G}_m$ gerbes over genus 1 curves derived 
 equivalent?  If $C$ and $C'$ are derived equivalent curves\, can we prove 
 that $C'$ is the moduli space of certain vector bundles on $C$?  If $C'=Pi
 c^d(C)$\, is it true that $C=Pic^f(C')$ for some $f$\, and if so\, can we 
 use Fourier-Mukai theory to find $f$? (Spoilers: when one is $Pic^d$ of th
 e other\; yes\; yes and yes.)  This is joint work with Soumya Sankar.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/1/
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