Derived Functor Cohomology groups with Yoneda Product

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology)
Sultana, Mariam (Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology)

Husain, Hafiz Syed, & Sultana, Mariam. (2021). DERIVED FUNCTOR COHOMOLOGY GROUPS WITH YONEDA PRODUCT. 한국수학교육학회지시리즈B:순수및응용수학, 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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Vol.28 No.2

DERIVED FUNCTOR COHOMOLOGY GROUPS WITH YONEDA PRODUCT

Derived Functor Cohomology groups with Yoneda Product

Abstract

한국수학교육학회지시리즈B:순수및응용수학