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SUMMARY:Caleb Springer
DTSTART:20220126T160000Z
DTEND:20220126T170000Z
DTSTAMP:20260418T064432Z
UID:LNTS/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/59/">Ev
 ery finite abelian group arises as the group of rational points of an ordi
 nary abelian variety over $\\mathbb{F}_2$\,  $\\mathbb{F}_3$\, and $\\math
 bb{F}_5$</a>\nby Caleb Springer as part of London number theory seminar\n\
 n\nAbstract\nWe will show that every finite abelian group arises as the gr
 oup of rational points of an ordinary abelian variety over a finite field 
 with 2\, 3 or 5 elements.  Similar results hold over finite fields of larg
 er cardinality.  On our way to proving these results\, we will view the gr
 oup of rational points of an abelian variety as a module over its endomorp
 hism ring. By describing this module structure in important cases\, we obt
 ain (a fortiori) an understanding of the underlying groups. Combining this
  description of structure with recent results on the cardinalities of grou
 ps of rational points of abelian varieties over finite fields\, we will de
 duce the main theorem. This work is joint with Stefano Marseglia.\n
LOCATION:https://researchseminars.org/talk/LNTS/59/
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