25 citations · 58 across the 21 of their papers we have counts for
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Cohomology with supports; idempotent pairs
Joseph Lipman
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…
Grothendieck Duality theories -- abstract and concrete, I: pseudo-coherent finite maps
Joseph Lipman
Grothendieck Duality -- the theory of the twisted inverse image pseudofunctor (-)^! over a suitable category of scheme-maps -- can be developed concretely, with emphasis on explici…
On the fundamental class of an essentially smooth scheme-map
Joseph Lipman, Amnon Neeman
Let f: X -> Z be a separated essentially-finite-type flat map of noetherian schemes, and δ: X --> X \times_Z X the diagonal map. The fundamental class C_f (globalizing residues) is…
Relation between two twisted inverse image pseudofunctors in duality theory
Srikanth B. Iyengar, Joseph Lipman, Amnon Neeman
Grothendieck duality theory assigns to essentially-finite-type maps f of noetherian schemes a pseudofunctor f^\times right-adjoint to Rf_*, and a pseudofunctor f^! agreeing with f^…
Bivariance, Grothendieck duality and Hochschild homology, II: the fundamental class of a flat scheme-map
Leovigildo Alonso Tarrío, Ana Jeremías López, Joseph Lipman
Fix a noetherian scheme S. For any flat map f: X->Y of separated essentially-finite-type perfect S-schemes we define a canonical derived-category map c(f):\H(X)->f^!\H(Y), the fund…
Bivariance, Grothendieck duality and Hochschild homology
Leovigildo Alonso Tarrío, Ana Jeremías López, Joseph Lipman
A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the ca…