Derived Functor Cohomology groups with Yoneda Product

Husain, Hafiz Syed; Husain, Hafiz Syed; Sultana, Mariam; Sultana, Mariam

doi:https://doi.org/10.7468/jksmeb.2021.28.2.187

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.28 No.2

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Derived Functor Cohomology groups with Yoneda Product

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2021, v.28 no.2, pp.187-198

https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.2.187

Husain, Hafiz Syed
Sultana, Mariam

Husain,, H. S. , & Sultana,, M. (2021). Derived Functor Cohomology groups with Yoneda Product. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 28(2), 187-198, https://doi.org/https://doi.org/10.7468/jksmeb.2021.28.2.187

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Abstract

This work presents an exposition of both the internal structure of derived category of an abelian category D*(𝓐) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D*(𝓐) as elements in appropriate cohomology groups along with their compositions with the help of Yoneda construction under the assumption that the homological dimension of D*(𝓐) is greater than or equal to 2. These computational settings will then be considered under sheaf cohomological context with a particular case from projective geometry.

keywords: derived category, triangulated category, Yoneda product, sheaf cohomology, smooth projective variety

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Article Contents

Vol.28 No.2

Derived Functor Cohomology groups with Yoneda Product

Abstract

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics