The Course topics will be sheaf theory (on topological and ringed spaces), homological algebra in abelian categories, derived functors, sheaf cohomology and applications.
- B. R. Tennison, Sheaf theory, LMS
- B. Iversen, Cohomology of sheaves, Springer Verlag
- M. Kashiwara, P. Schapira, Sheaves on manifolds, Springer Verlag
- C. Weibel, an introduction to homological algebra, CUP
Learning Objectives
Knowledge acquired:
Basics in sheaf cohomology and homological algebra
Competence acquired:
Basic tools in sheaf cohomology and homological algebra.
Skills acquired (at the end of the course):
Application of cohomology to geometry and analysis.
Prerequisites
Courses to be used as requirements (required and/or recommended)
Courses required: none
Courses recommended: any course in basic general topology.
Teaching Methods
CFU: 9
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 72
Hours reserved to private study and other indivual formative activities: 102
Hours for lectures: 72
Hours for laboratory: 0
Hours for laboratory-field/practice: 0
Seminars (hours): 0
Stages (hours): 0
Intermediate examinations (hours): 0
Further information
Attendance of lectures, practice and lab:
Not mandatory
Teaching tools:
None
Office hours:
To be announced, upon request by e-mail.
Contact:
E-mail: gabriele.vezzosi@unifi.it
luigi.verdiani@unifi.it
Web:
http://www.dma.unifi.it/~vezzosi/
Type of Assessment
Oral exam consisting of a short lecture on course's topics or nearby ones (to be assigned specifically to the student), together with a couple of exercises from corse's topics.
Course program
- Basic category theory
- Presehaves and sheaves. definition and basic operations; ringed spaces. Examples
- Homological algebra in an abelian category. Derived functors.
- Cohomology of sheaves.
- Definition of Cech cohomology. Comparison with sheaf cohomology. De Rham theorem. Examples and computations.