Tensorial schemes
Algebraic Geometry
2011-11-01 v1 Category Theory
Abstract
Jacob Lurie (arXiv:math/0412266) has shown that for geometric stacks X,Y every cocontinuous tensor functor F : Qcoh(X) -> Qcoh(Y) is the pullback of a morphism Y -> X under the additional assumption that F is tame. In this note we get rid of this assumption if X is a projective scheme. In general, we call a scheme X tensorial if every cocontinuous tensor functor Qcoh(X) -> Qcoh(Y) is induced by a unique morphism Y -> X, show that projective schemes are tensorial and tensorial schemes are closed under various operations.
Cite
@article{arxiv.1110.6523,
title = {Tensorial schemes},
author = {Martin Brandenburg},
journal= {arXiv preprint arXiv:1110.6523},
year = {2011}
}
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16 pages