Inductive graded rings, hyperfields and quadratic forms

TL;DR

This paper analyzes inductive graded rings to address Marshall's signature conjecture and explores their connections with hyperfields and special groups, advancing the algebraic understanding of quadratic forms.

Contribution

It provides a detailed analysis of inductive graded rings and links them to hyperfields and special groups, offering new insights into quadratic form theory.

Findings

Clarified the structure of inductive graded rings

Established connections between hyperfields and inductive graded rings

Advanced the algebraic approach to quadratic forms

Abstract

The goal of this work is twofold: (i) to provide a detailed analysis of some categories of inductive graded ring - a concept introduced in [DM98] in order to provide a solution of Marshall's signature conjecture in the algebraic theory of quadratic forms; (ii) apply this analysis to deepen the connections between the category of special hyperfields ([dARM22]) - equivalent to the category of special groups ([DM00]) and the categories of inductive graded rings.