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 of the p-part of the Selmer group of A over K. In the special case of a Z_p^d-extensio and A a constant ordinary variety, using Akashi series, we show how the Euler characteristic of the dual of the Selmer group is related to special values of a p-adic -function.

Euler characteristic and Akashi series for Selmer groups over global function fields

Andrea Bandini;
2018

Abstract

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 of the p-part of the Selmer group of A over K. In the special case of a Z_p^d-extensio and A a constant ordinary variety, using Akashi series, we show how the Euler characteristic of the dual of the Selmer group is related to special values of a p-adic -function.
Bandini, Andrea; Valentino, Maria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/932896
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