We formulate a number of related generalisations of the weight part of Serre's conjecture to
the case of GLn over an arbitrary number field, motivated by the formalism of the Breuil …

We present a new construction of the-adic local Langlands correspondence for via the
patching method of Taylor–Wiles and Kisin. This construction sheds light on the relationship …

We compute the reductions of irreducible crystalline two-dimensional representations of GQ
p of slope 1, for primes p≥ 5, and all weights. We describe the semisimplification of the …

Let G be a Q _p Q p-split reductive group with connected centre and Borel subgroup B= TN
B= TN. We construct a right exact functor D^ ∨ _ Δ D Δ∨ from the category of smooth …

We describe an algorithm to compute the reduction modulo p of a crystalline Galois
representation of dimension 2 of Gal (ℚ¯ p/ℚ p) with distinct Hodge–Tate weights via the …

Robert P. Langlands is a Canadian mathematician. He became professor at the Institute for
Advanced Study (IAS) of Princeton in 1972, and has received numerous awards, among …