AffiliationUniv Arizona, Dept Math
MetadataShow full item record
CitationCais, B. Math. Ann. (2018) 372: 781. https://doi.org/10.1007/s00208-017-1608-1
Rights© Springer-Verlag GmbH Deutschland 2017
Collection InformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at firstname.lastname@example.org.
AbstractWe construct the Lambda-adic de Rham analogue of Hida's ordinary Lambda-adic etale cohomology and of Ohta's Lambda-adic Hodge cohomology, and by exploiting the geometry of integral models of modular curves over the cyclotomic extension of Qp, we give a purely geometric proof of the expected finiteness, control, and Lambda-adic duality theorems. Following Ohta, we then prove that our Lambda-adic module of differentials is canonically isomorphic to the space of ordinary Lambda-adic cuspforms. In the sequel (Cais, Compos Math, to appear) to this paper, we construct the crystalline counterpart to Hida's ordinary Lambda-adic etale cohomology, and employ integral p-adic Hodge theory to prove Lambda-adic comparison isomorphisms between all of these cohomologies. As applications of our work in this paper and (Cais, Compos Math, to appear), we will be able to provide a " cohomological" construction of the family of (phi, Gamma)-modules attached to Hida's ordinary Lambda-adic etale cohomology by Dee (J Algebra 235(2), 636664, 2001), as well as a new and purely geometric proof of Hida's finiteness and control theorems. We are also able to prove refinements of the main theorems in Mazur and Wiles (Compos Math 59(2): 231-264, 1986) and Ohta (J Reine Angew Math 463: 49-98, 1995).
Note12 month embargo; published online: 26 December 2017
VersionFinal accepted manuscript
SponsorsNSA Young Investigator Grant [H98230-12-1-0238]; NSF RTG [DMS-0838218]