# Connectedness of the Balmer spectra of right bounded derived categories

## TL;DR

This paper investigates the topological properties, specifically connectedness and noetherianity, of the Balmer spectrum associated with the right bounded derived category of finitely generated modules over a commutative ring, building on Balmer's classification theorem.

## Contribution

It provides new insights into the topological structure of the Balmer spectrum in the context of derived categories of modules over commutative rings.

## Key findings

- Characterization of connectedness of the Balmer spectrum
- Conditions for noetherianity of the spectrum
- Extension of Balmer's theorem to derived categories

## Abstract

By virtue of Balmer's celebrated theorem, the classification of thick tensor ideals of a tensor triangulated category $\T$ is equivalent to the topological structure of its Balmer spectrum $\spc \T$. Motivated by this theorem, we discuss connectedness and noetherianity of the Balmer spectrum of a right bounded derived category of finitely generated modules over a commutative ring.