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arXiv · 1205.5945

On the Iwasawa Main conjecture of abelian varieties over function fields

King Fai Lai·Ignazio Longhi·Ki-Seng Tan·Fabien Trihan
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Abstract

We study a geometric analogue of the Iwasawa Main Conjecture for abelian varieties in the two following cases: constant ordinary abelian varieties over $Z_p^d$-extensions of function fields ($d\geq 1$) ramified at a finite set of places, and semistable abelian varieties over the arithmetic $Z_p$-extension of a function field. One of the tools we use in our proof is a pseudo-isomorphism relating the duals of the Selmer groups of $A$ and its dual abelian variety $A^t$. This holds as well over number fields and is a consequence of a quite general algebraic functional equation.

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King Fai Lai, Ignazio Longhi, Ki-Seng Tan, Fabien Trihan. 2012-05-27. On the Iwasawa Main conjecture of abelian varieties over function fields. https://arxiv.org/abs/1205.5945

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