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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]

Let A be an abelian variety defined over a global field F of positive characteristic p and let F / F be a Z p N -extension, unramified outside a finite set of places of F . Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the p -primary Selmer group of A . To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Z p d -extension F d / F and for any Z p d − 1 -extension contained in F d , and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Z p [ [ Gal ( F / F ) ] ] in the case A is a constant abelian variety. [ABSTRACT FROM AUTHOR]