# Hyperdescent and \'etale K-theory

## TL;DR

This paper explores the properties of étale K-theory, revealing its close relationship with Selmer K-theory and demonstrating its well-behaved nature without finiteness assumptions.

## Contribution

It establishes a connection between étale K-theory and noncommutative Selmer K-theory, and analyzes sheaves versus hypersheaves of spectra on étale sites.

## Key findings

- Étale K-theory closely approximates Selmer K-theory.
- Étale K-theory exhibits well-behaved properties without finiteness constraints.
- Detailed investigation of sheaves and hypersheaves on étale sites.

## Abstract

We study the \'etale sheafification of algebraic K-theory, called \'etale K-theory. Our main results show that \'etale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories. Consequently, we show that \'etale K-theory has surprisingly well-behaved properties, integrally and without finiteness assumptions. A key theoretical ingredient is the distinction, which we investigate in detail, between sheaves and hypersheaves of spectra on \'etale sites.