Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp010c483n01s
 Title: A Scholzian Approach to the Local Langlands Correspondence for $$\mathrm{GL}_n$$ over function fields Authors: Li, Daniel Advisors: Morel, Sophie M. Contributors: Taylor, Richard L. Department: Mathematics Class Year: 2017 Abstract: Let $$F$$ is a local field of characteristic $$p$$. Inspired by work of Scholze, we construct a map $$\pi\mapsto\sigma(\pi)$$ from irreducible smooth representations of $$\mathrm{GL}_n(F)$$ to $$n$$-dimensional Weil representations of $$F$$. We prove that this map uniquely satisfies a purely local compatibility condition on traces of a test function $$f_{\tau,h}$$, and we also prove that this map is compatible with parabolically inducing tensor products. It is expected that $$\pi\mapsto\sigma(\pi)$$ equals the local Langlands correspondence for $$\mathrm{GL}_n$$ over $$F$$, up to Frobenius semisimplification. URI: http://arks.princeton.edu/ark:/88435/dsp010c483n01s Type of Material: Princeton University Senior Theses Language: en_US Appears in Collections: Mathematics, 1934-2020