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只看該作者 · 發(fā)表于 2025-3-23 09:59:15

Introduction,Let . : . → . be a proper, surjective, smooth map of schemes, with all fibers equidimensional with dimension ., and let ω. = Ω.. Grotherndieck’s duality theory [RD, VII, 4.1] produces a trace map . which is an isomorphism when . has geometrically connected fibers. When . = 0, this is just the usual trace map ..

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只看該作者 · 發(fā)表于 2025-3-23 23:05:57

Chee Leok Goh MD, MMed, MRCP(UK), FRCPEllary 4.4.5. In general, we want to recover that (1.1.2) is an isomorphism under local freeness hypotheses on the higher direct images, as well as a suitable analogue with smoothness relaxed to the CM condition. This issue is handled in§ 5.1.

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只看該作者 · 發(fā)表于 2025-3-24 15:57:53

Duality Foundations, for dualizing sheaves is set up at the end of this chapter. This makes it possible to consider the base change compatibility of the trace map for proper CM morphisms, a problem we will address in Chapter 4.

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