Noncommutative Weil conjecture

In this article, following an insight of Kontsevich, we extend the Weil conjecture, as well strong form Tate from realm algebraic geometry to broad noncommutative setting dg categories. Moreover, establish a functional equation for Hasse-Weil zeta functions, compute l-adic and p-adic absolute values eigenvalues cyclotomic Frobenius, provide complete description category numerical motives in terms q-numbers. As first application, prove conjecture several cases: twisted schemes, Calabi-Yau categories associated hypersurfaces, gluings root stacks, (twisted) global orbifolds, finite-dimensional algebras. second alternative proof particular cases intersections two quadrics linear sections determinantal varieties.