2019/04/21 by Ashay Burungale, Laurent Clozel, Burungale, Ashay +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1904.09522
openalex publication_date 2019/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The deformation theory of ordinary representations of the absolute Galois groups of totally real number fields (over a finite field k) has been studied for a long time, starting with the work of Hida, Mazur and Tilouine, and continued by Wiles and others. Hida has studied the behaviour of these deformations when one considers the p-cyclotomic tower of extensions of the field. In the limit, one obtains a deformation ring R_∞ classifying the ordinary deformations of the (Galois group of) the p-cyclotomic extension. We show that if R_∞ is Noetherian and certain adjoint μ-invariants vanish (as is often expected), then R_∞ is free over the ring of Witt vectors of k.