We consider the family of irreducible crystalline representations of dimension of given by the for a fixed weight . We study the locus of the parameter where these representations have a given reduction modulo . We give qualitative results on this locus and show that for a fixed and it can be computed by determining the reduction modulo of for a finite number of values of the parameter . We also generalize these results to other Galois types.
"On the locus of $2$-dimensional crystalline representations with a given reduction modulo $p$." Algebra Number Theory 14 (3) 643 - 700, 2020. https://doi.org/10.2140/ant.2020.14.643