David Savitt
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View article: An elementary proof of Newman's eta-quotient theorem
An elementary proof of Newman's eta-quotient theorem Open
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(mz)^{r_m} to be a (weakly) holomorphic modular form of lev…
View article: Components of moduli stacks of two-dimensional Galois representations
Components of moduli stacks of two-dimensional Galois representations Open
In the article [CEGS20b], we introduced various moduli stacks of two-dimensional tamely potentially Barsotti–Tate representations of the absolute Galois group of a p -adic local field, as well as related moduli stacks of Breuil–Kisin modul…
View article: Irregular loci in the Emerton-Gee stack for GL_2
Irregular loci in the Emerton-Gee stack for GL_2 Open
Let K/Q_p be unramified. Inside the Emerton-Gee stack X_2, one can consider the locus of two-dimensional mod p representations of the absolute Galois group of K having a crystalline lift with specified Hodge-Tate weights. We study the case…
View article: Local geometry of moduli stacks of two-dimensional Galois representations
Local geometry of moduli stacks of two-dimensional Galois representations Open
We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, as well as their resolutions by moduli stacks of two-dimensional Breuil-Kisin modules with tame descent data. We stud…
View article: The geometric Breuil-Mézard conjecture for two-dimensional potentially Barsotti-Tate Galois representations
The geometric Breuil-Mézard conjecture for two-dimensional potentially Barsotti-Tate Galois representations Open
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 of two-dimensional mod p representations of the absolute Ga…
View article: Components of moduli stacks of two-dimensional Galois representations
Components of moduli stacks of two-dimensional Galois representations Open
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, as well as related moduli stacks of Breuil-Kisin modules wi…
View article: Moduli stacks of two-dimensional Galois representations
Moduli stacks of two-dimensional Galois representations Open
We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, and relate their geometry to the weight part of Serre's conjecture for GL(2).
View article: General Serre weight conjectures
General Serre weight conjectures Open
We formulate a number of related generalisations of the weight part of Serre’s conjecture to the case of GL _n over an arbitrary number field, motivated by the formalism of the Breuil–Mézard conjecture. We give evidence for these conjectur…
View article: Potentially Crystalline Lifts of Certain Prescribed Types
Potentially Crystalline Lifts of Certain Prescribed Types Open
We prove several results concerning the existence of potentially crystalline lifts of prescribed Hodge-Tate weights and inertial types of a given representation \overline{r}:G_{K}\to\mathrm{GL}_{n}(\overline{\Bbb{F}}_p) , where K/\Bbb Q_p …
View article: Potentially Crystalline Lifts of Certain Prescribed Types
Potentially Crystalline Lifts of Certain Prescribed Types Open
We prove several results concerning the existence of potentially crystalline lifts of prescribed Hodge--Tate weights and inertial types of a given representation $\rbar:GK\to\GLn(\Fpbar)$, where $K/\Qp$ is a finite extension. Some of these…