Building bridges between Tate conjectures and arithmetic invariants

TL;DR

This paper explores the relationships between Tate conjectures, algebraic cycles, and arithmetic invariants, clarifying their connections and implications in algebraic geometry and number theory.

Contribution

It establishes new links between Tate conjectures, motivic generalizations, and Nagao's conjecture, enhancing understanding of their interplay.

Findings

Clarified connections between Tate conjectures and arithmetic invariants

Linked algebraic cycles with motivic generalizations and Nagao's conjecture

Provided a framework for future research in algebraic geometry and number theory

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.