Scalar extensions of categorical resolutions of singularities |
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Authors: | Zhaoting Wei |
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Institution: | Kent State University at Geauga, 14111 Claridon-Troy Road, Burton, OH 44021, United States |
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Abstract: | 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 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 . 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 ≥1 over a non-algebraically closed field. |
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