Given a newform $f$ and choice of a prime $p$, Deligne and Serre constructed a semisimple two-dimensional residual (mod $p$) Galois representation associated to $f.$ It is profitable to study equivalence classes of lifts of this Galois representation to $\Bbb{GL}_2(A)$ for certain rings $A,$ which can be done using the deformation theory of Galois representations. Mazur proved that when the residual representation is absolutely irreducible, there is a universal deformation ring parameterizing equivalence classes of lifts of the residual representation; and, further, that we can impose certain conditions on the residual representation and still produce a universal deformation ring parameterizing equivalence classes of lifts of our residual representation satisfying those conditions. In this talk, we will discuss the deformation condition of being ordinary and the universal ordinary deformation ring.
Ordinary Modular Deformation Problems
Tori Day, Mount Holyoke College
2022 AWM Research Symposium
New EDGE (Enhancing Diversity in Graduate Education) PhDs Special Session: Pure and Applied talks by Women Math Warriors