A New Definition of the Steenrod Operations in Algebraic Geometry

TL;DR

This paper introduces a novel, scheme-intrinsic definition of Steenrod operations in algebraic geometry, expanding their applicability and providing a direct formula based solely on the scheme, with foundational properties established.

Contribution

It offers a new intrinsic definition of Steenrod operations in Chow theory for any prime p, independent of previous domain-specific results, and includes a direct computational formula.

Findings

Defined Steenrod operations for all primes p in Chow theory.

Proved basic properties of these operations from the new definition.

Provided a direct formula depending only on the scheme itself.

Abstract

The Steenrod operations (mod p) in Chow theory are defined for any prime p for a quasi-projective scheme, without appealing to the results of any domain but Milnor's K-theory. The new definition also gives a direct formula that depends only on the scheme itself. Additionally, basic properties of the operations are proved from the new definition. The idea is based on a construction of M. Rost.