TY - JOUR

T1 - Characteristic ideals and Selmer groups

AU - Bandini, Andrea

AU - Bars, Francesc

AU - Longhi, Ignazio

N1 - Publisher Copyright:
© 2015 Elsevier Inc..

PY - 2015/12/1

Y1 - 2015/12/1

N2 - Let A be an abelian variety defined over a global field F of positive characteristic p and let F/F be a ZpN-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. To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Zpd-extension Fd/F and for any Zpd-1-extension contained in Fd, and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Zp[[Gal(F/F)]] in the case A is a constant abelian variety.

AB - Let A be an abelian variety defined over a global field F of positive characteristic p and let F/F be a ZpN-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. To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Zpd-extension Fd/F and for any Zpd-1-extension contained in Fd, and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Zp[[Gal(F/F)]] in the case A is a constant abelian variety.

KW - Characteristic ideals

KW - Iwasawa theory

KW - Selmer groups

UR - http://www.scopus.com/inward/record.url?scp=84937140268&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2015.05.011

DO - 10.1016/j.jnt.2015.05.011

M3 - Article

AN - SCOPUS:84937140268

SN - 0022-314X

VL - 157

SP - 530

EP - 546

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -