3 papers
math.NT2019
Pseudo-representations of weight one are unramified
Frank Calegari, Joel Specter
We prove that the determinant (pseudo-representation) associated to the Hecke algebra of Katz modular forms of weight one and level prime to p is unramified at p.
math.NT2018
Polynomials with Surjective Arboreal Galois Representations Exist in Every Degree
Joel Specter
Let~ be a Hilbertian field of characteristic~. R.W.K. Odoni conjectured that for every positive integer~ there exists a polynomial~ of degree~ such that each…
math.NT2011
Galois Extensions of Height-One Commuting Dynamical Systems
Ghassan Sarkis, Joel Specter
We consider a dynamical system consisting of a pair of commuting power series, one noninvertible and another nontorsion invertible, of height one with coefficients in the -adic…