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ISSN : 1226-0657

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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<sup>*</sup>(&#x1D4D0;) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D<sup>*</sup>(&#x1D4D0;) 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<sup>*</sup>(&#x1D4D0;) 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

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

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