Search

Let A be an abelian variety defined over a global function field F of positive characteristic p and let K / F be a p -adic Lie extension with Galois group G . We provide a formula for the (truncated) Euler characteristic χ ( G , S e l A ( K ) p ) of the p -part of the Selmer group of A over K . In the special case G ≃ Z p d and A a constant ordinary variety, using Akashi series, we show how the Euler characteristic of the dual of S e l A ( K ) p is related to special values of a p -adic L -function. [ABSTRACT FROM AUTHOR]