14 citations · 27 across the 11 of their papers we have counts for
6 papers · 1 filter
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…
Semistable abelian Varieties over Q
Frank Calegari
We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over Q with good reduction outside primes dividing N. Our results are contingent on the…
Almost Rational Torsion Points on Semistable Elliptic Curves
Frank Calegari
If P is an algebraic point on a commutative group scheme A/K, then P is _almost_rational_ if no two non-trivial Galois conjugates sigma(P), tau(P), have sum equal to 2P. In this pa…
Slopes of overconvergent 2-adic modular forms
Kevin Buzzard, Frank Calegari
The slope of a p-adic overconvergent eigenform of weight k is the p-adic valuation of its U_p eigenvalue. We find the slope of all 2-adic finite slope overconvergent eigenforms of…
A counterexample to the Gouvea--Mazur conjecture
Kevin Buzzard, Frank Calegari
Gouvea and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this note, we exhibit explicit…