tt-geometry of Tate motives over algebraically closed fields

TL;DR

This paper explores the tensor triangular geometry of Tate motives over algebraically closed fields, providing a comprehensive description of their spectra and ideal classifications for specific base fields.

Contribution

It offers the first complete tensor triangular spectrum and thick tensor ideal classification for Tate motives over certain algebraically closed fields.

Findings

Complete description of the tensor triangular spectrum for these motives

Classification of thick tensor ideals over algebraically closed fields

Results applicable to algebraic numbers and algebraic closures of finite fields

Abstract

We study Tate motives with integral coefficients through the lens of tensor triangular geometry. For some base fields, including the field of algebraic numbers and the algebraic closure of a finite field, we arrive at a complete description of the tensor triangular spectrum and a classification of thick tensor ideals.