Galois Actions on $\ell$-adic Local Systems and Their Nearby Cycles: A Geometrization of Fourier Eigendistributions on the $p$-adic Lie Algebra $\mathfrak{sl}(2)$

Aaron Christie

In this thesis, two ${\bar{\mathbb{Q}}}_{\ell }$-local systems, ${}^{\circ }\mathcal{E}$ and ${}^{\circ }{\mathcal{E}}^{\prime }$ on the regular unipotent subvariet…