TY - CHAP

T1 - Foundations of grothendieck duality for diagrams of schemes

AU - Lipman, Joseph

AU - Hashimoto, Mitsuyasu

PY - 2009

Y1 - 2009

N2 - This is a polished version of notes begun in the late 1980s, largely available from my home page since then, meant to be accessible to mid-level graduate students. The first three chapters treat the basics of derived categories and functors, and of the rich formalism, over ringed spaces, of the derived functors, for unbounded complexes, of the sheaf functors ⊗, Hom, f* and f* (where f is a ringed-space map). Included are some enhancements, for concentrated (= quasi-compact and quasi-separated) schemes, of classical results such as the projection and Kudie;unneth isomorphisms. The fourth chapter presents the abstract foundations of Grothendieck Duality-existence and tor-independent base change for the right adjoint of the derived functor Rf* when f is a quasiproper map of concentrated schemes, the twisted inverse image pseudofunctor for separated finite-type maps of noetherian schemes, some refinements for maps of finite tor-dimension, and a brief discussion of dualizing complexes.

AB - This is a polished version of notes begun in the late 1980s, largely available from my home page since then, meant to be accessible to mid-level graduate students. The first three chapters treat the basics of derived categories and functors, and of the rich formalism, over ringed spaces, of the derived functors, for unbounded complexes, of the sheaf functors ⊗, Hom, f* and f* (where f is a ringed-space map). Included are some enhancements, for concentrated (= quasi-compact and quasi-separated) schemes, of classical results such as the projection and Kudie;unneth isomorphisms. The fourth chapter presents the abstract foundations of Grothendieck Duality-existence and tor-independent base change for the right adjoint of the derived functor Rf* when f is a quasiproper map of concentrated schemes, the twisted inverse image pseudofunctor for separated finite-type maps of noetherian schemes, some refinements for maps of finite tor-dimension, and a brief discussion of dualizing complexes.

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U2 - 10.1007/978-3-540-85420-3

DO - 10.1007/978-3-540-85420-3

M3 - Chapter

AN - SCOPUS:62649172677

SN - 9783540854197

T3 - Lecture Notes in Mathematics

SP - 1

EP - 482

BT - Foundations of Grothendieck Duality for Diagrams of Schemes

PB - Springer Verlag

ER -