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 language | English |
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Pages (from-to) | 298-306 |
Number of pages | 9 |
Journal | Journal of Number Theory |
Volume | 99 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2003 Apr 1 |
Externally published | Yes |
Keywords
- Abelian variety
- Brauer group
- Galois cohomology
- Wild ramification
- p-adic field
ASJC Scopus subject areas
- Algebra and Number Theory