2012/09/01 by Bryden Cais, Cais, Bryden · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11F33 #11F67 #11G18 #11R23 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11F33 #msc:11F67 #msc:11G18 #msc:11R23
paper · pdf · doi:10.48550/arxiv.1209.0046
openalex publication_date 2012/09/01 · arxiv created 2012/09/04 · arxiv updated 2012/09/05 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We construct Λ-adic de Rham and crystalline analogues of Hida's ordinary Λ-adic etale cohomology, and by exploiting the geometry of integral models of modular curves over the cyclotomic extension of \Qp, we prove appropriate finiteness and control theorems in each case. We then employ integral p-adic Hodge theory to prove Λ-adic comparison isomorphisms between our cohomologies and Hida's etale cohomology. As applications of our work, we provide a "cohomological" construction of the family of (ϕ,Γ)-modules attached to Hida's ordinary Λ-adic etale cohomology by Dee, and we give a new and purely geometric proof of Hida's finitenes and control theorems. We are also able to prove refinements of theorems of Mazur-Wiles and of Ohta; in particular, we prove that there is a canonical isomorphism between the module of ordinary Λ-adic cuspforms and the part of the crystalline cohomology of the Igusa tower on which Frobenius acts invertibly.