Building bridges between Tate conjectures and arithmetic invariants

Abstract

In this paper, we clarify and build connections between various conjectures largely motivated by the works of Jean-Pierre Serre and John Tate. We closely study the Tate conjecture for algebraic cycles as well as their motivic generalizations along with various links to Nagao's conjecture.

Theorem 2.4 and Theorem 2.6 should be described in an object-specific way. Hence the current stated results are incorrect.