BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jacob Tsimerman (University of Toronto)
DTSTART:20200408T190000Z
DTEND:20200408T200000Z
DTSTAMP:20260422T205614Z
UID:HarvardNT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HarvardNT/1/
 ">Bounding torsion in class groups and families of local systems</a>\nby J
 acob Tsimerman (University of Toronto) as part of Harvard number theory se
 minar\n\n\nAbstract\n(joint w/ Arul Shankar) We discuss a new method to bo
 und 5-torsion in class groups of quadratic fields using the refined BSD co
 njecture for elliptic curves. The most natural “trivial” bound on the 
 n-torsion is to bound it by the size of the entire class group\, for which
  one has a global class number formula. We explain how to make sense of th
 e n-torsion of a class group intrinsically as a selmer group of a Galois m
 odule. We may then similarly bound its size by the Tate-Shafarevich group 
 of an appropriate elliptic curve\, which we can bound using the BSD conjec
 ture. This fits into a general paradigm where one bounds selmer groups of 
 finite Galois modules by embedding into global objects\, and using class n
 umber formulas. If time permits\, we explain how the function field pictur
 e yields unconditional results and suggests further generalizations.\n
LOCATION:https://researchseminars.org/talk/HarvardNT/1/
END:VEVENT
END:VCALENDAR