Variance and Duality for Cousin Complexes on Formal Schemes.
Lipman, Joseph.
Variance and Duality for Cousin Complexes on Formal Schemes. - 1st ed. - 1 online resource (290 pages) - Contemporary Mathematics ; v.375 . - Contemporary Mathematics .
Intro -- Contents -- Preface -- Part 1. Pseudofunctorial behavior of Cousin complexes on formal schemes -- 1. Introduction and main results -- 2. Preliminaries on formal schemes -- 3. Local cohomology and Cousin complexes -- 4. Generalized fractions and pseudofunctors -- 5. Pseudofunctorial behavior for smooth maps -- 6. Closed immersions and base change -- 7. The retract case -- 8. The main theorem -- 9. Residual and dualizing complexes -- 10. Some explicit descriptions -- References -- Part 2. Duality for Cousin complexes -- 1. Introduction -- 1.1. Conventions -- 2. Traces -- 2.1. Local rings -- 2.2. Trace at the graded level -- 2.3. Relative projective space -- 2.4. The Trace Theorem -- 2.5. Traces and translations -- 3. The twisted inverse image pseudofunctor -- 3.1. Factorizations -- 3.2. Flat base change -- 3.3. Comparing pseudofunctors -- 4. The comparison map -- 4.1. Pseudo-proper maps -- 4.2. Étale base change -- 5. Smooth maps -- 5.1. Verdier's isomorphism -- 5.2. Smooth pseudo-finite maps -- 5.3. The isomorphism theorem for smooth maps -- 6. The Cousin of the comparison map -- 6.1. Definitions and notations -- 6.2. Closed immersions -- 6.3. General maps -- 7. The Comparison map for flat morphisms -- 7.1. Tor and Ext -- 7.2. Local cohomology and the twisted inverse image -- 8. The universal property of the trace -- 8.1. Duality for Cousin complexes -- 9. Variants -- 9.1. Preliminaries -- 9.2. Twisted inverse image via residual complexes -- 9.3. Comparison of the two twisted inverse images -- References -- Part 3. Pasting pseudofunctors -- 1. Introduction -- 2. The abstract pasting results -- 3. Proofs I (generalized isomorphisms in the labeled setup) -- 4. Proofs II (the cocycle condition) -- 5. Proofs III (old isomorphisms and linearity) -- 6. Proofs IV (the output) -- 7. Applications -- References -- Index.
9780821879658
Homology theory.
Abelian categories.
Duality theory (Mathematics).
Algebra, Homological.
Schemes (Algebraic geometry).
Electronic books.
QA612.3 -- .L568 2005eb
516.3/5
Variance and Duality for Cousin Complexes on Formal Schemes. - 1st ed. - 1 online resource (290 pages) - Contemporary Mathematics ; v.375 . - Contemporary Mathematics .
Intro -- Contents -- Preface -- Part 1. Pseudofunctorial behavior of Cousin complexes on formal schemes -- 1. Introduction and main results -- 2. Preliminaries on formal schemes -- 3. Local cohomology and Cousin complexes -- 4. Generalized fractions and pseudofunctors -- 5. Pseudofunctorial behavior for smooth maps -- 6. Closed immersions and base change -- 7. The retract case -- 8. The main theorem -- 9. Residual and dualizing complexes -- 10. Some explicit descriptions -- References -- Part 2. Duality for Cousin complexes -- 1. Introduction -- 1.1. Conventions -- 2. Traces -- 2.1. Local rings -- 2.2. Trace at the graded level -- 2.3. Relative projective space -- 2.4. The Trace Theorem -- 2.5. Traces and translations -- 3. The twisted inverse image pseudofunctor -- 3.1. Factorizations -- 3.2. Flat base change -- 3.3. Comparing pseudofunctors -- 4. The comparison map -- 4.1. Pseudo-proper maps -- 4.2. Étale base change -- 5. Smooth maps -- 5.1. Verdier's isomorphism -- 5.2. Smooth pseudo-finite maps -- 5.3. The isomorphism theorem for smooth maps -- 6. The Cousin of the comparison map -- 6.1. Definitions and notations -- 6.2. Closed immersions -- 6.3. General maps -- 7. The Comparison map for flat morphisms -- 7.1. Tor and Ext -- 7.2. Local cohomology and the twisted inverse image -- 8. The universal property of the trace -- 8.1. Duality for Cousin complexes -- 9. Variants -- 9.1. Preliminaries -- 9.2. Twisted inverse image via residual complexes -- 9.3. Comparison of the two twisted inverse images -- References -- Part 3. Pasting pseudofunctors -- 1. Introduction -- 2. The abstract pasting results -- 3. Proofs I (generalized isomorphisms in the labeled setup) -- 4. Proofs II (the cocycle condition) -- 5. Proofs III (old isomorphisms and linearity) -- 6. Proofs IV (the output) -- 7. Applications -- References -- Index.
9780821879658
Homology theory.
Abelian categories.
Duality theory (Mathematics).
Algebra, Homological.
Schemes (Algebraic geometry).
Electronic books.
QA612.3 -- .L568 2005eb
516.3/5