13 citations · 18 across the 5 of their papers we have counts for
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Elliptic Curves of Odd Modular Degree
Frank Calegari, Matthew Emerton
The modular degree m_E of an elliptic curve E/Q is the minimal degree of any surjective morphism X_0(N) -> E, where N is the conductor of E. We give a necessarily set of criteria f…
On the Ramification of Hecke Algebras at Eisenstein Primes
Frank Calegari, Matthew Emerton
Using the modularity technique of Wiles, we study the Hecke algebra of weight 2 and prime level N localized at the Eisenstein primes. On the way, we recover some results of Mazur (…
The Hecke Algebra T_k has Large Index
Frank Calegari, Matthew Emerton
Let T_k denote the Hecke algebra acting on newforms of weight k and level N. We prove that the power of p dividing the index of T_k inside its normalisation grows at least linearly…
Unit L-functions and a conjecture of Katz
Matthew Emerton, Mark Kisin
Let f: X -> Y be a separated morphism of schemes of finite type over a finite field of characteristic p, let Lambda be an artinian local Z_p-algebra with finite residue field, let…