Tate cohomology of Whittaker lattices and base change of generic representations of ${\mathrm{GL}}_n$

Sabyasachi Dhar, Santosh Nadimpalli

Let $p$ and $l$ be distinct odd primes and let $n\ge 2$ be a positive integer. Let $E$ be a finite Galois extension of degree $l$ of a $p$-adic field $F$. Let $q$ be the cardinali…