University of Chicago
When
2 – 3 p.m., Feb. 18, 2025
Where
Title: Criteria for pseudorepresentations to arise from genuine representations
Abstract: In application to modularity, one often seeks for an R=T theorem, that is, the deformation ring R is isomorphic to a (localized) Hecke algebra T. However, sometimes only the framed deformation ring exists. With the framing variables, it is obviously larger than the Hecke algebra. Pseudorepresentations, which is a generalization of the notion of traces of representations, was invented to get around this issue. We will introduce the notion of pseudorepresentations and discuss the criteria for pseudo representations to arise from genuine representations. Next, we will introduce the algorithm used to explicitly compute usual deformation rings and pseudodeformation rings for finitely presented groups, which leads to the discovery of a counterexample.