Local Duality with Dualizing Complexes and Other Dualities

2018 ◽  
pp. 295-316
Author(s):  
Peter Schenzel ◽  
Anne-Marie Simon
Keyword(s):  
Local Duality ◽  
Dualizing Complexes

On Grothendieck's local duality theorem

1979 ◽  
Vol 85 (3) ◽  
pp. 431-437 ◽  
Author(s):  
M. H. Bijan-Zadeh ◽  
R. Y. Sharp
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Noetherian Ring ◽  
Duality Theorem ◽  
Great Emphasis ◽  
Triangulated Category ◽  
Elementary Approach ◽  
Commutative Noetherian Ring ◽  
Local Duality ◽  
Dualizing Complexes

In (11) and (12), a comparatively elementary approach to the use of dualizing complexes in commutative algebra has been developed. Dualizing complexes were introduced by Grothendieck and Hartshorne in (2) for use in algebraic geometry; the approach to dualizing complexes in (11) and (12) differs from that of Grothendieck and Hartshorne in that it avoids use of the concepts of triangulated category, derived category, and localization of categories, and instead places great emphasis on the concept of quasi-isomorphism of complexes of modules over a commutative Noetherian ring.

Dualizing Complexes of Affine Semigroup Rings

1990 ◽  
Vol 322 (2) ◽  
pp. 561 ◽  
Author(s):  
Uwe Schafer ◽  
Peter Schenzel
Keyword(s):  
Semigroup Rings ◽  
Affine Semigroup ◽  
Dualizing Complexes

Hopf algebras with rigid dualizing complexes

2008 ◽  
Vol 169 (1) ◽  
pp. 89-108 ◽  
Author(s):  
D.-M. Lu ◽  
Q.-S. Wu ◽  
J. J. Zhang
Keyword(s):  
Hopf Algebras ◽  
Dualizing Complexes
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