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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
 M3//EN
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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20220627T093416Z
DTSTART:20220628T130000Z
DTEND:20220628T140000Z
SUMMARY:Celine Maistret (University of Bristol)  - Parity of ranks of abe
 lian surfaces
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}d1ra-l48dmo
 39-6uc32b
DESCRIPTION:Abstract : Let K be a number field and A/K an abelian surface
 . By the Mordell-Weil theorem\, the group of K-rational points on A is f
 initely generated and as for elliptic curves\, its rank is predicted by 
 the Birch and Swinnerton-Dyer conjecture. A basic consequence of this co
 njecture is the parity conjecture: the sign of the functional equation o
 f the L-series determines the parity of the rank of A/K. Assuming finite
 ness of the Shafarevich-Tate group\, we prove the parity conjecture for 
 principally polarized abelian surfaces under suitable local constraints.
  Using a similar approach  we show that for two elliptic curves E_1 and 
 E_2 over K with isomorphic 2-torsion\, the parity conjecture is true for
  E_1 if and only if it is true for E_2.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:B22\, Zochonis Building\, Manchester
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