Scalar extensions of categorical resolutions of singularities. (English) Zbl 1420.14041
Summary: Let \(X\) be a quasi-compact, separated scheme over a field \(k\) and we can consider the categorical resolution of singularities of \(X\). In this paper let \(k^\prime / k\) be a field extension and we study the scalar extension of a categorical resolution of singularities of \(X\) and we show how it gives a categorical resolution of the base change scheme \(X_{k^\prime}\). Our construction involves the scalar extension of derived categories of DG-modules over a DG algebra. As an application we use the technique of scalar extension developed in this paper to prove the non-existence of full exceptional collections of categorical resolutions for a projective curve of genus \(\geq 1\) over a non-algebraically closed field.
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 14E15 | Global theory and resolution of singularities (algebro-geometric aspects) |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
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