Growth of Fine Selmer Groups in Infinite Towers

Kundu, Debanjana

Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 921-936

Résumé

In this paper, we study the growth of fine Selmer groups in two cases. First, we study the growth of fine Selmer ranks in multiple $\mathbb{Z}_{p}$-extensions. We show that the growth of the fine Selmer group is unbounded in such towers. We recover a sufficient condition to prove the $\unicode[STIX]{x1D707}=0$ conjecture for cyclotomic $\mathbb{Z}_{p}$-extensions. We show that in certain non-cyclotomic $\mathbb{Z}_{p}$-towers, the $\unicode[STIX]{x1D707}$-invariant of the fine Selmer group can be arbitrarily large. Second, we show that in an unramified $p$-class field tower, the growth of the fine Selmer group is unbounded. This tower is non-Abelian and non-$p$-adic analytic.

Détail

DOI : 10.4153/S0008439520000168

Mots-clés : Iwasawa theory, fine Selmer groups, class groups, p-rank

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