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SUMMARY:Average Ranks of Elliptic Curves After p-Extension - Ross Paterson
  (University of Bristol)
DTSTART:20221025T133000Z
DTEND:20221025T143000Z
UID:TALK180401@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:As E varies among elliptic curves defined over the rational nu
 mbers\, a theorem of Bhargava and Shankar shows that the average rank of t
 he Mordell--Weil group E(Q) is bounded. If we now fix a number field K\, i
 s the same true of E(K)? I will report on progress on this question\, answ
 ering it in the affirmative for certain choices of K. This progress follow
 s from a statistical study of certain local invariants of elliptic curves\
 , which loosely describe the failure of Galois descent for the associated 
 p-Selmer groups.  Time permitting\, we will also discuss upper and lower b
 ounds for the average dimension of 2-Selmer groups over multi-quadratic ex
 tensions.\n
LOCATION:Centre for Mathematical Sciences\, MR13
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