Families over the integral Bernstein Center and Tate cohomology of local Base change lifts for GL(n, F)

Sabyasachi Dhar, Santosh Nadimpalli

Let $p$ and $l$ be distinct odd primes, and let $F$ be a $p$-adic field. Let $\pi$ be a generic smooth integral representation of ${\mathrm{GL}}_n(F)$ over an ${\overline{\mathbb{Q}}}_l$-ve…