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- TOBY GEE, TONG LIU, DAVID SAVITT
- 2012

Let p > 2 be prime. We prove the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the unramified case (that is, the Buzzard–Diamond–Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. This completes the analysis begun in [BLGG11], which proved that all… (More)

- DAVID SAVITT
- 2002

We prove a portion of a conjecture of B. Conrad, F. Diamond, and R. Taylor, yielding some new cases of the Fontaine-Mazur conjectures, specifically, the modularity of certain potentially Barsotti-Tate Galois representations. The proof follows the template of Wiles, Taylor-Wiles, and Breuil-Conrad-Diamond-Taylor, and relies on a detailed study of the… (More)

- TOBY GEE, DAVID SAVITT
- 2010

We study the possible weights of an irreducible 2-dimensional modular mod p representation of Gal(F /F), where F is a totally real field which is totally ramified at p, and the representation is tamely ramified at the prime above p. In most cases we determine the precise list of possible weights; in the remaining cases we determine the possible weights up… (More)

- TOBY GEE, TONG LIU, DAVID SAVITT
- 2011

Let p > 2 be prime. We complete the proof of the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the totally ramified case, by proving that any weight which occurs is a predicted weight. Our methods are a mixture of local and global techniques, and in the course of the proof we establish some purely local results… (More)

- MATTHEW EMERTON, DAVID SAVITT
- 2013

We prove the main conjectures of [Bre12] (including a generali-sation from the principal series to the cuspidal case) and [Dem], subject to a mild global hypothesis that we make in order to apply certain R = T theorems. More precisely, we prove a multiplicity one result for the mod p cohomology of a Shimura curve at Iwahori level, and we show that certain… (More)

- DAVID SAVITT
- 2009

We study the possible weights of an irreducible 2-dimensional mod p representation of Gal(F /F) which is modular in the sense of that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field. In most cases we determine the precise list of possible weights; in… (More)

Motivated by Gauss's first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that… (More)

- DAVID SAVITT
- 2006

For every polynomial f of degree n with no double roots, there is an associated family C(f) of harmonic algebraic curves, fibred over the circle, with at most n−1 singular fibres. We study the combinatorial topology of C(f) in the generic case when there are exactly n − 1 singular fibres. In this case, the topology of C(f) is determined by the data of an… (More)

Our aim in this paper is to prove that a smooth geometrically irreducible curve C of genus 4 over the finite field F 8 may have at most 25 F 8-points. Our strategy is as follows: if C has more than 18 F 8-points, then C may not be hyperelliptic, and so the canonical divisor of C yields an embedding of C into P 3 F 8. The image of C under this embedding is a… (More)

- DAVID SAVITT
- 2004

We prove a conjecture of Conrad, Diamond, and Taylor on the size of certain deformation rings parametrizing potentially Barsotti-Tate Ga-lois representations. To achieve this, we extend results of Breuil and Mézard (classifying Galois lattices in semistable representations in terms of " strongly divisible modules ") to the potentially crystalline case in… (More)