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SUMMARY:The p-parity conjecture for elliptic curves with a p-isogeny
DTSTART:20120816T111500
DTEND:20120816T123000
DTSTAMP:20260925T093934Z
UID:db7fc86875d102096a776d7c9251ce31f951341e6b76670a033f328d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Kestutis Cesnavicius\nFor an elliptic curve E over a number fi
 eld K\, one consequence of the Birch and Swinnerton-Dyer conjecture is the
  parity conjecture: the global root number\nmatches the parity of the Mord
 ell-Weil rank. Assuming finiteness of the pprimary part of Sha(E/K) for a 
 prime p\, this is equivalent to the p-parity conjecture: the global root n
 umber matches the parity of the Z_p-corank of the pinfinity Selmer group. 
 We prove the latter unconditionally for E that have a Krational p-isogeny.
  We deduce that the p-parity conjecture holds for every E with complex mul
 tiplication defined over K\, and that for such E\, if the p-primary part o
 f Sha(E/K) is infinite\, it must contain (Q_p/Z_p)^2.
LOCATION:AAC006 http://plan.epfl.ch/?zoom=20&recenter_y=5864224.42038&rece
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 nem
STATUS:CONFIRMED
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