Counting local systems via the trace formula
Yuval Z. Flicker Β· Journal fΓΌr die reine und angewandte Mathematik (Crelles Journal) Β· 2015
Abstract Let π½ q {\mathbb{F}_{q}} be a finite field with q elements, π½ \mathbb{F} = = π½ Β― q \overline{\mathbb{F}}_{q} an algebraic closure of π½ q {\mathbb{F}_{q}} , X 1 {X_{1}} an absolutely irreducible projective smooth curve over π½ q {\mathbb{F}_{q}} , and S 1 {S_{1}} a finite set of closed points of X 1 {X_{1}} . Let N 1 {N_{1}} be the cardinality of S 1 {S_{1}} . Erasing the index 1 indicates extension of scalars to π½ {\mathbb{F}} . Replacing it by m indicates extension of scalars to π½ q m \mathbb{F}_{q^{m}} β \subset