Structure of ordinary $\Lambda$-adic arithmetic cohomology groups

Jaehoon Lee

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arXiv · 1811.07235

Structure of ordinary $\Lambda$-adic arithmetic cohomology groups

Jaehoon Lee

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Abstract

We study the $\Lambda$-module structure of the ordinary parts of the arithmetic cohomology groups of modular Jacobians made out of various towers of modular curves. We prove that the ordinary parts of $\Lambda$-adic Selmer groups coming from two different towers have "almost same" $\Lambda$-module structures. We also prove the cotorsionness of $\Lambda$-adic Tate-Shafarevich group under mild assumptions.

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Jaehoon Lee. 2018-11-17. Structure of ordinary $\Lambda$-adic arithmetic cohomology groups. https://arxiv.org/abs/1811.07235

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