Characteristic ideals and Selmer groups

2014/04/10 by Bandini, Andrea, Bars, Francesc, Longhi, Ignazio
#11G35 #11R23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1404.2788

Abstract

Let A be an abelian variety defined over a global field F of positive characteristic p and let \calf/F be a \Z_p^\N-extension, unramified outside a finite set of places of F. Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the p-primary Selmer group of A, in order to formulate an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra \Z_p[[\Gal(\calf/F)]] (which we also prove for a constant abelian variety). To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a \Z_p^d-extension \calf_d/F and for any \Z_p^d-1-extension contained in \calf_d , and then use a limit process.

Related

• Selmer groups over \Z_p^d-extensions
• Non-commutative Iwasawa theory of abelian varieties over global function fields
• Characteristic ideals and Iwasawa theory
• The algebra ℤ_ℓ[[ℤ_p^d]] and applications to Iwasawa theory
• On the Iwasawa Main conjecture of abelian varieties over function fields