7 papers · 1 filter
Prescribed lifts of 2-dimensional representations
Matthew Emerton, Toby Gee, Lue Pan +1
Let F be a totally real field, and let p be prime. Under standard Taylor--Wiles hypotheses, we show that an irreducible, 2-dimensional, totally odd mod p representation of the abso…
A categorical p-adic Langlands correspondence for GL_2(Q_p)
Andrea Dotto, Matthew Emerton, Toby Gee
Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a d…
Localization of smooth p-power torsion representations of GL_2(Q_p)
Andrea Dotto, Matthew Emerton, Toby Gee
We show that the category of smooth representations of GL_2(Q_p) on p-power torsion modules localizes over a certain projective scheme, and give some applications.
An introduction to the categorical p-adic Langlands program
Matthew Emerton, Toby Gee, Eugen Hellmann
We give an introduction to the "categorical" approach to the p-adic Langlands program, in both the "Banach" and "analytic" settings.
Explicit reciprocity laws and Iwasawa theory for modular forms
Matthew Emerton, Robert Pollack, Tom Weston
We prove that the Mazur-Tate elements of an eigenform sit inside the Fitting ideals of the corresponding dual Selmer groups along the cyclotomic -extension (up to…
Components of moduli stacks of two-dimensional Galois representations
Ana Caraiani, Matthew Emerton, Toby Gee +1
In a previous article we introduced various moduli stacks of two-dimensional tamely potentially Barsotti-Tate representations of the absolute Galois group of a p-adic local field,…