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Lim, Meng Fai
- mH(G)-Property and Congruence of Galois Representations
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1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, CN
1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, CN
Source
Journal of the Ramanujan Mathematical Society, Vol 33, No 1 (2018), Pagination: 37-74Abstract
In this paper, we study the Selmer groups of two congruent Galois representations over an admissible p-adic Lie extension. We will show that under appropriate congruence condition, if the dual Selmer group of one satisfies the mH(G)-property, so will the other. In the event that the mH(G)-property holds, and assuming certain further hypothesis on the decomposition of primes in the p-adic Lie extension, we compare the ranks of the π-free quotient of the two dual Selmer groups. We then apply our results to compare the characteristic elements attached to the Selmer groups. We also study the variation of the ranks of the π-free quotient of the dual Selmer groups of specialization of a big Galois representation. We emphasis that our results do not assume the vanishing of the μ-invariant.
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- On the Complete Faithfulness of the P-Free Quotient Modules of Dual Selmer Groups
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Authors
Affiliations
1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, CN
1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, CN
Source
Journal of the Ramanujan Mathematical Society, Vol 32, No 3 (2017), Pagination: 299–326Abstract
In this paper, we consider the question of the complete faithfulness of the p-free quotient module of the dual Selmer groups of elliptic curves defined over a noncommutative p-adic Lie extension. Our question will refine previous questions on the complete faithfulness of dual Selmer groups. We also consider the question of the triviality of the central torsion submodules of these Iwasawa modules and we see that this latter question is intimately related to the former. We will also formulate and study analogous questions for the dual Selmer groups of Hida deformations. We then give positive answer to our questions, and establish “control theorem” results between the questions.- The Growth of Fine Selmer groups
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Authors
Affiliations
1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, CN
2 Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, CA
1 School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, CN
2 Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, CA
Source
Journal of the Ramanujan Mathematical Society, Vol 31, No 1 (2016), Pagination: 79–94Abstract
Let A be an abelian variety defined over a number field F. In this paper, we will investigate the growth of the p-rank of the fine Selmer group in three situations. In particular, in each of these situations, we show that there is a strong analogy between the growth of the p-rank of the fine Selmer group and the growth of the p-rank of the class groups.- On the Homology of Iwasawa Cohomology Groups
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Authors
Affiliations
1 Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario M5S 2E4, CA
1 Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario M5S 2E4, CA