arXiv: Number Theory | 2019
Galois symbol maps for abelian varieties over a $p$-adic field
Abstract
We study the Galois symbol map associated to the multiplicative group and an abelian variety which has good ordinary reduction over a $p$-adic field. As a byproduct, one can calculate the class group in the view of the class field theory for curves over a $p$-adic field.