Cohomology operations and algebraic geometry

TL;DR

This paper provides an overview of Voevodsky's approach to constructing categories related to algebraic varieties, emphasizing their connection to cohomology operations and algebraic invariants.

Contribution

It summarizes the motivations and foundational ideas behind Voevodsky's categories that link algebraic geometry with homotopy theory.

Findings

Highlights the relationship between algebraic varieties and homotopy categories.

Explains how these categories preserve algebraic invariants.

Provides insights into the motivations for Voevodsky's constructions.

Abstract

The manuscript is an overview of the motivations and foundations lying behind Voevodsky's ideas of constructing categories similar to the ordinary topological homotopy categories. The objects of these categories are strictly related to algebraic varieties and preserve some of their algebraic invariants.