Derived Functor Cohomology groups with Yoneda Product
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
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.
참고문헌 (19)
- C. Bartocci, "Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics", Progress in Mathematics, 276 (2009)
- A. Bondal, "Generators and Representability of Funcors in Com-mutative and Non-Commutative Geometry", Mosc. Math. J., 3, pp.1~36 (2003)
- H. Cartan, "Homological Algebra" (1956), Princeton University Press
- S.I. Gelfand, "Springer Monographs in Mathematics" (2003), Springer-Verlag
- J. Harris, "Graduate Texts in Mathematics" (1992), Springer-Verlag
- R. Hartshorne, "Graduate Texts in Mathematics" (1977), Springer-Verlag
- R. Hartshorne, "Lecture Notes in Mathematics" (1966), Springer-Verlag
- D. Huybrechts, "Oxford Mathemati-cal Monographs" (2006), Oxford University Press
- B. Iversen, "Cohomology of Sheaves" (1986), Springer-Verlag
- S. Katz, "D-Branes, Orbifolds and Ext Groups", Nuclear Physics B, 673, pp.263~300 (2003)
- M. Kontsevich, "Homological Algebra of Mirror Symmetry", Proceedings of the Inter-national Congress of Mathematicians, 1995, pp.120139~ (1994)
- S.M. Lane, "Categories for the Working Mathematician" (1971), Springer-Verlag
- B. Lian, "Mirror Principles-I", Asian J. Math, 1, pp.729~763 (1997)
- B. Lian, "Mirror Principles-II", Asian J. Math, 3, pp.109~146 (1999)
- B. Lian, "Mirror Principles-III", Asian J. Math, 3, pp.771~800 (1999)
- B. Lian, "Mirror Principles-IV", Surv. Diff. Geom. VII, 2000, pp.475~496 (2000)
- D. Orlov, "Derived Categories of Coherent Sheaves and equivalences between them", Russian Math. Surveys, 58, pp.511~591 (2003)
- R. Thomas, "Derived Categories for the Working Mathematicians", ~ (2001)
- C.A. Weibel, "An Introduction to Homological Algebra" (1994), Cambridge University Press