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Affine space over triangulated categories: a further invitation to Grothendieck derivators

Paul Balmer, John Zhang

Abstract

We propose a construction of affine space (or "polynomial rings") over a triangulated category, in the context of stable derivators.

Affine space over triangulated categories: a further invitation to Grothendieck derivators

Abstract

We propose a construction of affine space (or "polynomial rings") over a triangulated category, in the context of stable derivators.

Paper Structure

This paper contains 5 sections, 6 theorems, 7 equations.

Table of Contents

  1. Introduction
  2. A glimpse at derivators
  3. Statement of the result
  4. The proof
  5. The scheme case

Key Result

Theorem 2

Let $R$ be a ring and consider the category of chain complexes $\mathscr M=\mathop{\mathrm{Ch}}\nolimits(R\text{-}\mathop{\mathrm{Mod}}\nolimits)$ with weak-equivalences the quasi-isomorphisms. Then formula eq:Ho defines a derivator that we shall denote by $\mathbb{D}\mathrm{er}(R\text{-}\mathop{\ma

Theorems & Definitions (14)

  • Theorem 2: Grothendieck
  • Definition 3
  • Theorem 5
  • Corollary 6
  • Lemma 8
  • proof
  • Definition 9
  • Remark 10
  • Proposition 11
  • proof
  • ...and 4 more