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Inclusions between p-bounded crystalline loci in dimension two
Kalyani Kansal, Brandon Levin, David Savitt
The paper investigates the reduced special fibers of the Emerton‑Gee stack of two‑dimensional crystalline Galois representations as the Hodge type varies over p‑bounded types, clas…
An elementary proof of Newman's eta-quotient theorem
David Savitt
Let eta(z) be the Dedekind eta function. Newman studied the modularity of eta-quotients, giving necessary and sufficient conditions for a function of the form \prod_{0 < m | N} eta…
Components of moduli stacks of two-dimensional Galois representations
Ana Caraiani, Matthew Emerton, Toby Gee +1
In a previous article we introduced various moduli stacks of two-dimensional tamely potentially Barsotti-Tate representations of the absolute Galois group of a p-adic local field,…
The geometric Breuil-Mézard conjecture for two-dimensional potentially Barsotti-Tate Galois representations
Ana Caraiani, Matthew Emerton, Toby Gee +1
We establish a geometrisation of the Breuil-Mézard conjecture for potentially Barsotti-Tate representations, as well as of the weight part of Serre's conjecture, for moduli stacks…