Remarks on Euler class groups and two conjectures

TL;DR

This paper revisits the theory of Euler class groups, broadening its scope, and discusses recent results and potential improvements related to two conjectures by Asok-Fasel.

Contribution

It generalizes the theory of Euler class groups and offers insights and possible enhancements to existing results on two conjectures.

Findings

Broadened the scope of Euler class groups

Provided remarks on two Asok-Fasel results

Suggested potential improvements to existing theorems

Abstract

We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.