Structure of ordinary Λ-adic arithmetic cohomology groups

2018/11/17 by Jaehoon Lee, Lee, Jaehoon
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.NT

paper · pdf · doi:10.48550/arxiv.1811.07235

30pages

arxiv created 2018/11/17 · openalex publication_date 2018/11/17 · arxiv updated 2018/11/20 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We study the Λ-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 Λ-adic Selmer groups coming from two different towers have "almost same" Λ-module structures. We also prove the cotorsionness of Λ-adic Tate-Shafarevich group under mild assumptions.

Citations

• Structure of Mordell-Weil groups over ℤ_p-extensions

Related

• Congruences of modular forms and modularity of Tate-Shafarevich classes
• Relative completed cohomologies and modular symbols
• Critical Lambda-adic modular forms and bi-ordinary complexes
• The Geometry of Hida Families and Λ-adic Hodge Theory
• Structure of Mordell-Weil groups over ℤ_p-extensions