122 citations · 901 across the 71 of their papers we have counts for
7 papers · 1 filter
Constructing elliptic curves from Galois representations
Andrew Snowden, Jacob Tsimerman
Given a non-isotrivial elliptic curve over an arithmetic surface, one obtains a lisse -adic sheaf of rank two over the surface. This lisse sheaf has a number of straightforwa…
Residual irreducibility of compatible systems
Stefan Patrikis, Andrew Snowden, Andrew Wiles
We show that if is a compatible system of absolutely irreducible Galois representations of a number field then the residual representation is abs…
Counting elliptic curves with prescribed torsion
Robert Harron, Andrew Snowden
Mazur's theorem states that there are exactly 15 possibilities for the torsion subgroup of an elliptic curve over the rational numbers. We determine how often each of these groups…
Singularities of ordinary deformation rings
Andrew Snowden
Let R^univ be the universal deformation ring of a residual representation of a local Galois group. Kisin showed that many loci in MaxSpec(R^univ[1/p]) of interest are Zariski close…
Real components of modular curves
Andrew Snowden
We study the real components of modular curves. Our main result is an abstract group-theoretic description of the real components of a modular curve defined by a congruence subgrou…
Bigness in compatible systems
Andrew Snowden, Andrew Wiles
Clozel, Harris and Taylor have recently proved a modularity lifting theorem of the following general form: if rho is an l-adic representation of the absolute Galois group of a numb…