f-categories and Tate motives

TL;DR

This paper demonstrates that the triangulated category of Tate motives over a field algebraic over the rationals is equivalent to the bounded derived category of its heart, using Beilinson's f-category theory.

Contribution

It establishes an equivalence between Tate motives and derived categories, answering a question posed by Levine.

Findings

Triangulated category of Tate motives is equivalent to bounded derived category of its heart.

The result applies when the base field is algebraic over the rationals.

Provides a new approach using Beilinson's f-category theory.

Abstract

Using Beilinson's theory of f-categories, we prove that the triangulated category of Tate motives over a field k is equivalent to the bounded derived category of its heart, provided that k is algebraic over the rationals. This answers a question asked by Levine.