Some observations about motivic tensor triangulated geometry over a finite field

TL;DR

This paper explores the structure of tensor triangulated geometry within motivic categories, focusing on the conjectural spectrum of the stable homotopy category over finite fields, providing insights into its theoretical framework.

Contribution

It offers new observations on the conjectural structure of the tensor triangulated spectrum in motivic categories over finite fields, connecting tensor triangulated geometry with motivic homotopy theory.

Findings

Insights into the conjectural spectrum structure over finite fields

Connections between motivic categories and tensor triangulated geometry

Preliminary observations guiding future research

Abstract

We give a brief introduction to tensor triangulated geometry, a brief introduction to various motivic categories, and then make some observations about the conjectural structure of the tensor triangulated spectrum of the Morel-Voevodsky stable homotopy category over a finite field.