Sheaves and Supplying Homological Algebra, NRU HSE, Spring 2018

РУССКАЯ ВЕРСИЯ ЭТОЙ СТРАНИЦЫ
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Alexey Gorodentsev's
SHEAVES AND SUPPLYING HOMOLOGICAL ALGEBRA
Spring 2018

Contents:
Preliminary program
Recomended Textbooks
Home Tasks
Marking Rules and Exam

Recomended Textbooks

V.I.Danilov. Cohomology of Algebraic Manifolds. In: Algebraic Geometry II: Cohomology of Algebraic Varieties. Algebraic Surfaces. Encyclopaedia of Mathematical Sciences. Book 35. Springer (1995).

P.Griffiths, J.Harris. Principles of Algebraic Geometry.

S.I.Gelfand, Yu.I.Manin. Methods of Homological Algebra. Part I.

B.Iversen. Cohomology of Sheaves.

C.A.Weibel. An Introduction to Homological Algebra.

Here are some lecture notes:
Introduсtion to categories and fuctors.

The problems are either obligatory or honorary (optional). The obligatory problems are those not marked with stars from the tasks numbered by integers. The problems marked with stars and all problems from the tasks numbered by non-integers (e.g., 2½) are honorary. The maximal final mark «10» can be achieved without solving the honorary problems.

Task 1: Categories and Functors.
Task 2: Adjoint Functors, Exact Functors, and Colimits.
Task 2½ [honorary]. Diagrams in Exact Categories.
Task 3. Reminder on Complexes and Their (Co)homologies.
Task 4. Spectral Sequences.
Task 5. Abelian Sheaves on Paracompact Spaces. (Updated 5.04.2018)
Task 6. Sections with a Compact Support.
Task 7. Cohomologies of (quasi)coherent sheaves.
Task 8. Direct images with proper supports.

Marking rules and Exam

Let H and E be the total amounts of problems you have solved among the Home Tasks and during the Written Exam, both computed as percentage [total number of solved problems]:[total number of obligatory problems], which may be >100 if you solved honorary problems. Your final mark is computed as min(140,H+E)/14 by means of the standard rounding-off rule.