Finite u Invariant and Bounds on Cohomology Symbol Lengths

TL;DR

This paper proves that fields with finite u invariant have bounded symbol lengths in their μ₂ cohomology across all degrees, addressing a question posed by Parimala.

Contribution

It establishes a universal bound on cohomology symbol lengths for fields with finite u invariant, advancing understanding in algebraic cohomology.

Findings

Fields with finite u invariant have bounded symbol lengths in μ₂ cohomology.

Provides a positive answer to Parimala's question.

Enhances the theoretical framework of cohomological bounds.

Abstract

In this note we answer a question of Parimala's, showing that fields with finite $u$ invariant have bounds on the symbol lengths in their $\mu_2$ cohomology in all degrees.