Extended powers and Steenrod operations in algebraic geometry

TL;DR

This paper develops a framework for constructing Steenrod operations in algebraic geometry applicable to generalized cohomology theories with order-two formal group laws, extending previous work in motivic cohomology and Chow rings.

Contribution

It introduces a new setting for Steenrod operations in algebraic geometry for theories with order-two formal group laws, adapting methods from cobordism and cohomology.

Findings

Provides a unified construction framework for Steenrod operations in algebraic geometry.

Extends the applicability of Steenrod operations to new cohomology theories.

Adapts techniques from unoriented cobordism and mod 2 cohomology.

Abstract

Steenrod operations have been defined by Voedvodsky in motivic cohomology in order to show the Milnor and Bloch-Kato conjectures. These operations have also been constructed by Brosnan for Chow rings. The purpose of this paper is to provide a setting for the construction of the Steenrod operations in algebraic geometry, for generalized cohomology theories whose formal group law has order two. We adapt the methods used by Bisson-Joyal in studying Steenrod and Dyer-Lashof operations in unoriented cobordism and mod 2 cohomology.