Presentism and Eternalism in Perspective

The distinction between presentism and eternalism is usually sought in some formula like ‘Only presently existing things exist’ or ‘Past, present, and future events are equally real’. I argue that ambiguities in the copula prevent these slogans from distinguishing significant opposed positions. I suggest in addition that one can find a series of significant distinctions if one takes spacetime structure into account. These presentisms and eternalisms are not contradictory. They are complementary elements of a complete naturalistic philosophy of time

The Buzzard-Diamond-Jarvis conjecture for unitary groups

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 predicted Serre weights occur. Our methods are purely local, using the theory of (phi,Ghat)-modules to determine the possible reductions of certain two-dimensional crystalline representations.Comment: J. Amer. Math. Soc., to appear. Contains minor corrections from published versio

Potentially crystalline lifts of certain prescribed types

We prove several results concerning the existence of potentially crystalline lifts with prescribed Hodge-Tate weights and inertial types of a given n-dimensional mod p representation of the absolute Galois group of K, where K/Q_p is a finite extension. Some of these results are proved by purely local methods, and are expected to be useful in the application of automorphy lifting theorems. The proofs of the other results are global, making use of automorphy lifting theorems.Comment: 22 pages; final version, to appear in Document