Sheaf Theory

Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties.

B. R. Tennison (Author)

9780521207843, Cambridge University Press

Paperback, published 18 December 1975

176 pages
22.8 x 15.2 x 1.1 cm, 0.269 kg

Sheaf theory provides a means of discussing many different kinds of geometric objects in respect of the connection between their local and global properties. It finds its main applications in topology and modern algebraic geometry where it has been used as a tool for solving, with great success, several long-standing problems. This text is based on a lecture course for graduate pure mathematicians which builds up enough of the foundations of sheaf theory to give a broad definition of manifold, covering as special cases the algebraic geometer's schemes as well as the topological, differentiable and analytic kinds, and to define sheaf cohomology for application to such objects. Exercises are provided at the end of each chapter and at various places in the text. Hints and solutions to some of them are given at the end of the book.

1. Presheaves and their stalks
2. Sheaves and Sheaf Spaces
3. Morphisms of Sheaves and Presheaves
4. Ringed Spaces
5. Cohomology

Subject Areas: Algebra [PBF]