Relative Integral Functors for Singular Fibrations and Singular Partners

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dc.creatorRuipérez, D. Hernández
dc.creatorMartín, A. C. López
dc.creatorde Salas, F. Sancho
dc.date2006-10-10
dc.date2007-09-24
dc.date.accessioned2026-07-07T08:31:36Z
dc.date.available2026-07-07T08:31:36Z
dc.descriptionWe study relative integral functors for singular schemes and characterise those which preserve boundness and those which have integral right adjoints. We prove that a relative integral functor is an equivalence if and only if its restriction to every fibre is an equivalence. This allows us to construct a non-trivial auto-equivalence of the derived category of an arbitrary genus one fibration with no conditions on either the base or the total space and getting rid of the usual assumption of irreducibility of the fibres. We also extend to Cohen-Macaulay schemes the criterion of Bondal and Orlov for an integral functor to be fully faithful in characteristic zero and give a different criterion which is valid in arbitrary characteristic. Finally, we prove that for projective schemes both the Cohen-Macaulay and the Gorenstein conditions are invariant under Fourier-Mukai functors.
dc.descriptionFinal version to appear in Journal of the European Mathematical Society. Some proofs have been modified using referee's suggestions
dc.identifierhttps://arxiv.org/abs/math/0610319
dc.identifierhttp://arxiv.org/abs/math/0610319
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138547
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject18E30 (Primary) ; 14F05, 14J27, 14E30, 13D22, 14M05 (Secondary)
dc.titleRelative Integral Functors for Singular Fibrations and Singular Partners
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