## Speaker:

Geoffrey Akers

## Institution:

CUNY Graduate Center

## Time:

Thursday, May 20, 2021 - 3:00pm

## Location:

Zoom https://uci.zoom.us/j/97940217018

We consider a crystalline universal deformation ring R of an n-dimensional, mod p Galois representation whose semisimplification is the direct sum of two non-isomorphic absolutely irreducible representations. Under some hypotheses, we obtain that R is a discrete valuation ring. The method examines the ideal of reducibility of R, which is used to construct extensions of representations in a Selmer group with specified dimension. This can be used to deduce modularity of representations.