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SUMMARY:Enis Kaya (KU Leuven)
DTSTART:20240405T124000Z
DTEND:20240405T134000Z
DTSTAMP:20260423T021247Z
UID:OBAGS/45
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OBAGS/45/">p
 -adic Integration Theories on Curves</a>\nby Enis Kaya (KU Leuven) as part
  of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nFor curves ove
 r the field of p-adic numbers\, there are two notions of p-adic integratio
 n: Berkovich-Coleman integrals which can be performed locally\, and Vologo
 dsky integrals with desirable number-theoretic properties. These integrals
  have the advantage of being insensitive to the reduction type at p\, but 
 are known to coincide with Coleman integrals in the case of good reduction
 . Moreover\, there are practical algorithms available to compute Coleman i
 ntegrals.\n\nBerkovich-Coleman and Vologodsky integrals\, however\, differ
  in general. In this talk\, we give a formula for passing between them. To
  do so\, we use combinatorial ideas informed by tropical geometry. We also
  introduce algorithms for computing Berkovich-Coleman and Vologodsky integ
 rals on hyperelliptic curves of bad reduction. By covering such a curve by
  certain open spaces\, we reduce the computation of Berkovich-Coleman inte
 grals to the known algorithms on hyperelliptic curves of good reduction. W
 e then convert the Berkovich-Coleman integrals into Vologodsky integrals u
 sing our formula. We illustrate our algorithm with a numerical example.\n\
 nThis talk is partly based on joint work with Eric Katz from the Ohio Stat
 e University.\n
LOCATION:https://researchseminars.org/talk/OBAGS/45/
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