Categorical base loci and Orlov spectra

In this proposal we initiate the theory of categorical base loci. We introduce the idea of building the following analogies: 1) The analogy between classical linear system and certain functor of a category. 2) The second analogy is between base loci of a linear system and categorical base loci. We propose a theory of categorical multiplier ideal sheaves. Our approach is based on the pioneering works by Seidel Ein, Lazarsfeld, Mustata, Nakamaye, Popa, Budur The main ideas of the project is that the gaps in the Orlov spectra can be seen as jump numbers of a multiplier ideal sheaf. If completed this idea will lead to the solution of some classical questions in Algebraic Geometry.

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