Growth of Fine Selmer Groups in Infinite Towers
Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 921-936
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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.
Mots-clés :
Iwasawa theory, fine Selmer groups, class groups, p-rank
Kundu, Debanjana. Growth of Fine Selmer Groups in Infinite Towers. Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 921-936. doi: 10.4153/S0008439520000168
@article{10_4153_S0008439520000168,
author = {Kundu, Debanjana},
title = {Growth of {Fine} {Selmer} {Groups} in {Infinite} {Towers}},
journal = {Canadian mathematical bulletin},
pages = {921--936},
year = {2020},
volume = {63},
number = {4},
doi = {10.4153/S0008439520000168},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000168/}
}
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