Syst\`emes de points dans les dg-cat\'egories satur\'ees

B. Toën; M. Vaquié

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arXiv · 1504.07748

Syst\`emes de points dans les dg-cat\'egories satur\'ees

B. Toën·M. Vaquié

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Abstract

In this work we consider the question of realizing triangulated dg-categories by derived categories of algebraic varieties. For this, we introduce the notion of "system of points" in saturated dg-categories. We show that given such a system on a dg-category T, we can construct an algebraic space M, of finite type, smooth and separated, together with a dg-functor from T to a certain twisted dg-category of sheaves on M. We prove that this functor is furthermore an equivalence if and only if M is proper. All along this work we study t-strutcures on algebraic families of objects in T, which might be of independant interest.

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BibTeX RIS

B. Toën, M. Vaquié. 2015-04-29. Syst\`emes de points dans les dg-cat\'egories satur\'ees. https://arxiv.org/abs/1504.07748

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