HIGHER ALGEBRA
Stampa
Enrollment year
2018/2019
Academic year
2019/2020
Regulations
DM270
Academic discipline
MAT/02 (ALGEBRA)
Department
DEPARTMENT OF PHYSICS
Course
Curriculum
Fisica teorica
Year of study
Period
1st semester (30/09/2019 - 17/01/2020)
ECTS
6
Lesson hours
48 lesson hours
Language
Italian
Activity type
ORAL TEST
Teacher
CANONACO ALBERTO (titolare) - 6 ECTS
Prerequisites
The contents of the courses: Algebra 1, Linear Algebra and Geometry 1.
Learning outcomes
The aim of the course is to provide an introduction to homological algebra.
Course contents
(Left or right) modules over a (noncommutative) ring; bimodules; operations on modules; tensor product of modules.
Categories, functors and natural transformations; (co)limits in a category; adjoint functors. (Pre)additive categories and abelian categories; (left and/or right) exact functors. Injective and projective objects in an abelian category; resolutions; derived functors.
Injective, projective and flat modules; Ext and Tor functors; dimension theory for modules and rings. Cohomology of groups. Sheaves on a topological space and cohomology of sheaves.
Teaching methods
Lectures
Reccomended or required readings
P. Aluffi, "Algebra: chapter 0", Graduate Studies in Mathematics 104, American Mathematical Society, 2009.
S. Bosch, "Algebraic Geometry and Commutative Algebra", Universitext, Springer, 2013.
R. Godement, "Topologie algébrique et théorie des faisceaux", Hermann, 1973
P.J. Hilton, U. Stammbach, "A Course in Homological Algebra", second edition, Graduate Texts in Mathematics 4, Springer-Verlag, 1997.
S. Mac Lane, "Categories for the Working Mathematician", second edition, Graduate Texts in Mathematics 5, Springer-Verlag, 1998.
M.S. Osborne, "Basic Homological Algebra", Graduate Texts in Mathematics 196, Springer-Verlag, 2000.
C.A. Weibel, "An Introduction to Homological Algebra", Cambridge University Press, 1994.
Assessment methods
The exam consists of an oral examination, during which the student must answer some questions, mainly of a theoretical nature.
Further information
Sustainable development goals - Agenda 2030