A proof of the generalized geometric boundary theorem using filtered spectra

TL;DR

This paper corrects and proves a generalized geometric boundary theorem using filtered spectra, refining Behrens' previous work and providing a more rigorous formulation of the theorem.

Contribution

It offers a corrected and formal proof of Behrens' generalized geometric boundary theorem employing the framework of filtered spectra.

Findings

Fixes a mistake in Behrens' original formulation.

Provides a rigorous proof using filtered spectra.

Clarifies the relationship between classical and generalized boundary theorems.

Abstract

In [Beh12, Lem. A.4.1], Behrens generalized the classical geometric boundary theorem [Rav86, Thm. 2.3.4]. In this article, we will reformulate [Beh12, Lem. A.4.1] to fix a mistake made by Behrens, and prove it using the language of filtered spectra.