Classifying subcategories, local algebra and the Rosenberg spectrum of a locally noetherian category

Abhishek Banerjee

Classifying subcategories, local algebra and the Rosenberg spectrum of a locally noetherian category

Category Theory 2023-02-22 v4 Commutative Algebra Rings and Algebras

Authors: Abhishek Banerjee

Abstract

Let $\mathcal A$ be a locally noetherian Grothendieck category. In this paper, we study subcategories of $\mathcal A$ using subsets of the Rosenberg spectrum $\mathfrak Spec(\mathcal A)$ . Along the way, we also develop results in local algebra with respect to the category $\mathcal A$ that we believe to be of independent interest.

Keywords

locally noetherian category Grothendieck category subcategories Rosenberg spectrum local algebra classifying subcategories

Cite

@article{arxiv.1710.08068,
  title  = {Classifying subcategories, local algebra and the Rosenberg spectrum of a locally noetherian category},
  author = {Abhishek Banerjee},
  journal= {arXiv preprint arXiv:1710.08068},
  year   = {2023}
}

Comments

Paper heavily updated

Classifying subcategories, local algebra and the Rosenberg spectrum of a locally noetherian category

Abstract

Keywords

Cite

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