On tate duality for Jacobian varieties

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Abstract

Let A be an abelian variety over a p-adic field k and At its dual. The group of k-rational point A(k) has a p-adic decreasing filtration U A(k). When A = J is a Jacobian variety, we give a precise description of the exact annihilator of Un A(k) with respect to the Tate pairing A(k) × H1 (k, At) → ℚ/ℤ. As an application, we give another proof of the result of McCallum in the special case A = J, which says that Un A(k) annihilates ker(H1 (k, At) → H1 (k′, At)) whenever k′/k is a finite extension of conductor ≤n.

Original languageEnglish
Pages (from-to)298-306
Number of pages9
JournalJournal of Number Theory
Volume99
Issue number2
DOIs
Publication statusPublished - 2003 Apr 1

Keywords

  • Abelian variety
  • Brauer group
  • Galois cohomology
  • Wild ramification
  • p-adic field

ASJC Scopus subject areas

  • Algebra and Number Theory

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