By Colin J. Bushnell
If F is a non-Archimedean neighborhood box, neighborhood type box concept should be considered as giving a canonical bijection among the characters of the multiplicative crew GL(1,F) of F and the characters of the Weil workforce of F. If n is a favorable integer, the n-dimensional analogue of a personality of the multiplicative team of F is an irreducible delicate illustration of the final linear staff GL(n,F). The neighborhood Langlands Conjecture for GL(n) postulates the life of a canonical bijection among such gadgets and n-dimensional representations of the Weil crew, generalizing category box theory.
This conjecture has now been proved for all F and n, however the arguments are lengthy and depend upon many deep principles and methods. This publication provides an entire and self-contained facts of the Langlands conjecture within the case n=2. it's geared toward graduate scholars and at researchers in similar fields. It presupposes no distinct wisdom past the beginnings of the illustration idea of finite teams and the constitution conception of neighborhood fields. It makes use of basically neighborhood equipment, with out entice harmonic research on adele teams.