The weight filtration for real algebraic varieties

TL;DR

This paper constructs a weight filtration for real algebraic varieties by extending the concept of weight complexes from complex varieties, providing a new tool for analyzing their Borel-Moore homology.

Contribution

It introduces a filtered chain complex, the weight complex, for real algebraic varieties, generalizing the weight filtration concept from complex algebraic geometry.

Findings

Defines the weight complex for real algebraic varieties

Establishes the well-definedness up to filtered quasi-isomorphism

Induces a weight filtration on Borel-Moore homology with Z/2 coefficients

Abstract

Using the work of Guillen and Navarro Aznar we associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on Borel-Moore homology with Z/2 coefficients an analog of the weight filtration for complex algebraic varieties.