Pontryagin duality for Iwasawa modules and abelian varieties

2014/06/23 by King Fai Lai, Ignazio Longhi, Lai, King Fai +5
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1406.5815

Abstract

We prove a functional equation for two projective systems of finite abelian p-groups, \\fa_n\ and \\fb_n\, endowed with an action of \ZZ_p^d such that \fa_n can be identified with the Pontryagin dual of \fb_n for all n. Let K be a global field. Let L be a \ZZ_p^d-extension of K (d≥ 1), unramified outside a finite set of places. Let A be an abelian variety over K. We prove an algebraic functional equation for the Pontryagin dual of the Selmer group of A.

Related

• Functional equations for supersingular abelian varieties over Z_p²-extensions
• On the Iwasawa Main conjecture of abelian varieties over function fields
• Characteristic ideals and Selmer groups
• Pontryagin duality for varieties over p-adic fields
• Selmer groups over \Z_p^d-extensions