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arXiv · 1401.7222

On derived categories and noncommutative motives of varieties

A. Khan Yusufzai
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Abstract

In this short note we show how results of Orlov and Toën imply that any equivalence between the derived categories of coherent sheaves on two varieties lifts to an equivalence at the level of dg-categories. This establishes the link between the noncommutative geometry practised by the school of Bondal-Orlov, and the variant developed by Kontsevich and Tabuada. As an application we recover Orlov's result that the derived category determines the Chow motive with rational coefficients up to Tate twists.

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A. Khan Yusufzai. 2014-01-28. On derived categories and noncommutative motives of varieties. https://arxiv.org/abs/1401.7222

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