On the Iwasawa Main conjecture of abelian varieties over function fields

2012/05/27 by King Fai Lai, Ignazio Longhi, Lai, King Fai +5 · 1 citation
Mathematics · #11G10 #11R23 #11R58 #11S40 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1205.5945

openalex publication_date 2012/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ 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.

Citations

• Finding large Selmer rank via an arithmetic theory of local constants

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• Control Theorems for l-adic Lie extensions of global function fields

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