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SUMMARY:Local non-abelian Kummer maps for curves - Alexander Betts (Max Pl
 anck)
DTSTART:20190312T143000Z
DTEND:20190312T153000Z
UID:TALK118210@talks.cam.ac.uk
CONTACT:Beth Romano
DESCRIPTION:The non-abelian Kummer map associated to a variety X is a cert
 ain function which relates the Diophantine geometry of X to its etale fund
 amental group\, and appears for example in the non-abelian Chabauty method
  of Minhyong Kim. In this talk\, I will outline work in progress with Neta
 n Dogra\, providing a completely explicit description of the p-adic non-ab
 elian Kummer map for a curve X over an l-adic field (l different from p) i
 n terms of harmonic analysis on its reduction graph. In particular\, we ob
 tain a description of the local components of p-adic height functions on X
  in terms of the combinatorial height pairing on its reduction graph\, the
 reby removing one of the current limitations on the explicit quadratic Cha
 bauty method of Balakrishnan and Dogra.
LOCATION:MR13
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