The Tate Local Duality Theorem

2020 ◽  
pp. 131-143
Author(s):  
David Harari
Keyword(s):  
Duality Theorem ◽  
Local Duality

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.

A local duality theorem for categories of modules

1998 ◽  
Vol 89 (2) ◽  
pp. 1122-1126
Author(s):  
M. B. Zvyagina
Keyword(s):  
Duality Theorem ◽  
Local Duality

Local duality theorem for q-ary 1-perfect codes

2012 ◽  
Vol 70 (3) ◽  
pp. 305-311 ◽  
Author(s):  
Soohak Choi ◽  
Jong Yoon Hyun ◽  
Hyun Kwang Kim
Keyword(s):  
Duality Theorem ◽  
Perfect Codes ◽  
Local Duality

scholarly journals LOCAL DUALITY FOR THE SINGULARITY CATEGORY OF A FINITE DIMENSIONAL GORENSTEIN ALGEBRA

2020 ◽  
pp. 1-24
Author(s):  
DAVE BENSON ◽  
SRIKANTH B. IYENGAR ◽  
HENNING KRAUSE ◽  
JULIA PEVTSOVA
Keyword(s):  
Prime Ideal ◽  
Commutative Ring ◽  
Duality Theorem ◽  
Hochschild Cohomology ◽  
Local Duality ◽  
Singularity Category ◽  
Gorenstein Algebra ◽  
Finite Dimensional ◽  
Perfect Complexes ◽  
Serre Duality

A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the $\mathfrak{p}$ -local and $\mathfrak{p}$ -torsion subcategories of the derived category, for each homogeneous prime ideal $\mathfrak{p}$ arising from the action of a commutative ring via Hochschild cohomology.

Relative Canonical Modules and Some Duality Results

2019 ◽  
Vol 26 (02) ◽  
pp. 351-360 ◽  
Author(s):  
Majid Rahro Zargar
Keyword(s):  
Local Ring ◽  
Duality Theorem ◽  
Local Rings ◽  
Local Duality ◽  
Duality Results

Let (R, m) be a relative Cohen–Macaulay local ring with respect to an ideal a of R and set c to be ht a. We investigate some properties of the Matlis dual of the R-module [Formula: see text], and we show that such modules behave like canonical modules over Cohen–Macaulay local rings. Moreover, we provide some duality and equivalence results with respect to the module [Formula: see text], and these results lead us to achieve generalizations of some known results, such as the local duality theorem, which have been provided over a Cohen–Macaulay local ring admiting a canonical R-module.

On the Monge-Kantorovitch Duality Theorem

2001 ◽  
Vol 45 (2) ◽  
pp. 350-356 ◽  
Author(s):  
D. Ramachandran ◽  
L. Rüschendorf
Keyword(s):  
Duality Theorem

scholarly journals The Eilenberg-Borsuk duality theorem

1972 ◽  
Vol 75 (1) ◽  
pp. 68-72 ◽  
Author(s):  
J.M Aarts ◽  
T Nishiura
Keyword(s):  
Duality Theorem

scholarly journals A Fenchel-Rockafellar type duality theorem for maximization

1979 ◽  
Vol 20 (2) ◽  
pp. 193-198 ◽  
Author(s):  
Ivan Singer
Keyword(s):  
Convex Space ◽  
Duality Theorem ◽  
Locally Convex Space ◽  
Bounded Subset ◽  
Convex Functional ◽  
Lower Semi ◽  
Locally Convex

We prove that sup(f-h)(E) = sup(h*-f*)(E*), where f is a proper lower semi-continuous convex functional on a real locally convex space E, h: E → = [-∞, +∞] is an arbitrary-functional and, f*, h* are their convex conjugates respectively. When h = δG, the indicator of a bounded subset G of E, this yields a formula for sup f(G).

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