Joseph Lipman
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View article: Cohomology with supports; idempotent pairs
Cohomology with supports; idempotent pairs Open
This chapter sets out preliminaries for the duality theory in later chapters. An underlying idea is that local cohomology functors are higher derived functors of colocalizations (a.k.a.~coreflections). Predominantly well-known facts about …
View article: Grothendieck Duality theories -- abstract and concrete, I: pseudo-coherent finite maps
Grothendieck Duality theories -- abstract and concrete, I: pseudo-coherent finite maps Open
Grothendieck Duality -- the theory of the twisted inverse image pseudofunctor (-)^! over a suitable category of scheme-maps -- can be developed concretely, with emphasis on explicit constructions, or abstractly, with emphasis on category-t…
View article: On the fundamental class of an essentially smooth scheme-map
On the fundamental class of an essentially smooth scheme-map Open
Let f: X -> Z be a separated essentially-finite-type flat map of noetherian\nschemes, and \\delta: X --> X \\times_Z X the diagonal map. The fundamental class\nC_f (globalizing residues) is a map from the relative Hochschild functor\nL\\de…