King Fai Lai, Ignazio Longhi, Ki-Seng Tan, Fabien Trihan
Published 2012-05-27, updated 2013-04-26Version 2
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.
Comments: 80 pages; many relevant changes all over the paper from v1. Among the most significant ones: new introduction; proof of the functional equation for Gamma systems in more cases and some applications to CM abelian varieties
The Iwasawa Main conjecture of constant ordinary abelian varieties over function fields
Comparison of the $μ$-invariants of an abelian variety and its dual abelian variety
On a Noncommutative Iwasawa Main Conjecture for Function Fields
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