A classification of the irreducible mod-p representations of U(1,1)(Qₚ²/Qₚ)

Original · EN

Let p be a prime number. We classify all smooth irreducible mod-p representations of the unramified unitary group U(1,1)(Qₚ²/Qₚ) in two variables. We then investigate Langlands parameters in characteristic p associated to U(1,1)(Qₚ²/Qₚ), and propose a correspondence between certain equivalence classes of Langlands parameters and certain isomorphism classes of semisimple L-packets on U(1,1)(Qₚ²/Qₚ).