Let A be an abelian variety defined over a global field F of positive characteristic p and let \mathcal{F}/F be a Z_p^\infty-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 Z_p^d-extension \mathcal{F}_d/F and for any Z_p^{d−1}-extension contained in \mathcal{F}_d, and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Z_p[[Gal(\mathcal{F}/F)]] in the case A is a constant abelian variety.

Characteristic ideals and Selmer groups / Bandini, Andrea; Bars, Francesc; Longhi, Ignazio. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 157:(2015), pp. 530-546. [10.1016/j.jnt.2015.05.011]

### Characteristic ideals and Selmer groups

#### Abstract

Let A be an abelian variety defined over a global field F of positive characteristic p and let \mathcal{F}/F be a Z_p^\infty-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 Z_p^d-extension \mathcal{F}_d/F and for any Z_p^{d−1}-extension contained in \mathcal{F}_d, and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Z_p[[Gal(\mathcal{F}/F)]] in the case A is a constant abelian variety.
##### Scheda breve Scheda completa Scheda completa (DC)
Characteristic ideals and Selmer groups / Bandini, Andrea; Bars, Francesc; Longhi, Ignazio. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 157:(2015), pp. 530-546. [10.1016/j.jnt.2015.05.011]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2795174
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