The Local Langlands Correspondence for GL n over p-adic fields

The local Langlands conjecture for GL(n) over a p-adic field

The local Langlands conjecture for GL(n) over a p-adic field, n < p.

MAXIMAL VARIETIES AND THE LOCAL LANGLANDS CORRESPONDENCE FOR GL(n)

The cohomology of the Lubin-Tate tower is known to realize the local Langlands correspondence for GL(n) over a nonarchimedean local field. In this article we make progress towards a purely local proof of this fact. To wit, we find a family of formal schemes V such that the generic fiber of V is isomorphic to an open subset of Lubin-Tate space at infinite level, and such that the middle cohomolo...

THE LOCAL LANGLANDS CORRESPONDENCE FOR GLn OVER A p-ADIC FIELD

The Local Langlands Conjecture posits the existence of a bijection between certain classes of irreducible representations of a reductive group G, such as GLnpKq, and certain ndimensional representations of an additive extension of the Weil group WK (closely related to the Galois group). Here we focus solely on the case G “ GLn and K is a p-adic field (such as Qp). The Local Langlands conjecture...

ON REPRESENTATION THEORY OF GL(n) OVER p-ADIC DIVISION ALGEBRA AND UNITARITY IN JACQUET-LANGLANDS CORRESPONDENCE

Let F be a p-adic field of characteristic 0, and let A be an F -central division algebra of dimension dA over F . In the paper we first develop the representation theory of GL(m,A), assuming that holds the conjecture which claims that unitary parabolic induction is irreducible for GL(m,A)’s. Among others, we obtain the formula for characters of irreducible unitary representations of GL(m,A) in ...

The Jacquet-Langlands correspondence via `-adic uniformization