# The Balmer spectrum of Voevodsky motives and pure symbols

## TL;DR

This paper introduces new invariants for points in the Balmer spectrum of Voevodsky motives, linking them to Milnor K-theory, and studies their topological properties, including closure and boundary types.

## Contribution

It defines invariants of Balmer spectrum points using Milnor K-theory and explores their topological behavior, such as closure of isotropic points and boundary classifications.

## Key findings

- Isotropic points of the spectrum are closed.
- Boundary type points include isotropic points but exclude the etale point.
- Invariants relate spectrum points to pure symbols in Milnor K-theory.

## Abstract

In this article we introduce invariants of points of the Balmer spectrum of the Voevodsky motivic category whose values are "light Rost cycle submodules" of the module of pure symbols in Milnor's K-theory (mod 2). As an application, we show that isotropic points of the Balmer spectrum are closed. We also introduce the notion of points of a boundary type and show that this class contains isotropic points, but not the etale one.