28 citations · 115 across the 14 of their papers we have counts for
15 papers
Eisenstein congruences in tame families and the class group of a metabelian extension
Catherine Hsu, Alice Pozzi, Preston Wake +1
Ribet's 1976 proof of the converse to Herbrand's theorem created a new paradigm in algebraic number theory by illustrating that unramified abelian Galois extensions of number field…
Critical Lambda-adic modular forms and bi-ordinary complexes
Francesc Castella, Carl Wang-Erickson
We produce a flat -module of -adic critical slope overconvergent modular forms, producing a Hida-type theory that interpolates such forms over -adically varying integer we…
Moduli stacks of Galois representations and the -adic local Langlands correspondence for
Christian Johansson, James Newton, Carl Wang-Erickson
We give a categorical formulation of the -adic local Langlands correspondence for ,as an embedding of the derived category of locally admissible rep…
Explicit non-Gorenstein R=T via rank bounds II: Computational aspects
Catherine Hsu, Preston Wake, Carl Wang-Erickson
This is the second in a pair of papers about residually reducible Galois deformation rings with non-optimal level. In the first paper, we proved a Galois-theoretic criterion for th…
Explicit non-Gorenstein R=T via rank bounds I: Deformation theory
Catherine Hsu, Preston Wake, Carl Wang-Erickson
Ribet has proven remarkable results about non-optimal levels of residually reducible Galois representations. We focus on a non-optimal level that is the product of two distinct…
Higher Yoneda product structures and Iwasawa algebras modulo
Carl Wang-Erickson
We give answers to three questions posed by Sorensen. These concern the relationship between the modulo Iwasawa algebra of a torsionfree pro- group and -algebra st…
Presentations of non-commutative deformation rings via -algebras and applications to deformations of Galois representations and pseudorepresentations
Carl Wang-Erickson
We introduce an -algebra structure on the Hochschild cohomology of the endomorphism bimodule of a finite-dimensional representation of an associative algebra. We prove th…
Class groups and local indecomposability for non-CM forms
Francesc Castella, Carl Wang-Erickson, Haruzo Hida
In the late 1990's, R. Coleman and R. Greenberg (independently) asked for a global property characterizing those -ordinary cuspidal eigenforms whose associated Galois representa…
The Eisenstein ideal with squarefree level
Preston Wake, Carl Wang-Erickson
We use pseudodeformation theory to study the analogue of Mazur's Eisenstein ideal with certain squarefree levels. Given a prime number and a squarefree number satisfying…
Deformation conditions for pseudorepresentations
Preston Wake, Carl Wang-Erickson
Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur's Galois deformation theory for representations with that prope…
The rank of Mazur's Eisenstein ideal
Preston Wake, Carl Wang-Erickson
We use pseudodeformation theory to study Mazur's Eisenstein ideal. Given prime numbers and , we study the Eisenstein part of the -adic Hecke algebra for . We co…
A Harder-Narasimhan theory for Kisin modules
Brandon Levin, Carl Wang-Erickson
We develop a Harder-Narasimhan theory for Kisin modules generalizing a similar theory for finite flat group schemes due to Fargues. We prove the tensor product theorem, i.e., that…
Ordinary pseudorepresentations and modular forms
Preston Wake, Carl Wang-Erickson
In this short note, we observe that the techniques of our recent work "Pseudo-modularity and Iwasawa theory" can be used to provide a new proof of some of the residually reducible…
Pseudo-modularity and Iwasawa theory
Preston Wake, Carl Wang-Erickson
We prove, assuming Greenberg's conjecture, that the ordinary eigencurve is Gorenstein at an intersection point between the Eisenstein family and the cuspidal locus. As a corollary,…
Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
Carl Wang-Erickson
We construct and study the moduli of continuous representations of a profinite group with integral -adic coefficients. We present this moduli space over the moduli space of cont…