Scheda programma d'esame
ISTITUZIONI DI ALGEBRA
ANDREA MAFFEI
Anno accademico2016/17
CdSMATEMATICA
Codice134AA
CFU9
PeriodoPrimo semestre
LinguaItaliano

ModuliSettoreTipoOreDocente/i
ISTITUZIONI DI ALGEBRAMAT/02LEZIONI63
ANDREA MAFFEI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
The student who successfully completes the course will will be aware of integral extensions of rings and of dimension theory of local noetherian rings. He/she will know what is a completion of a ring or of a module, he/she will be aware of the relations of commutative algebra with algebraic geometry; The student will also know what is a category and a functor and will be able to work with some of the most important functors in homological algebra and algebraic topology, i.e. the derived functors Tor^n and Ext^n. he will be able to compute the cohomology of some groups.
Assessment criteria of knowledge
During the oral exam the student must be able to demonstrate his/her knowledge of the course material and be able to discuss the reading matter thoughtfully and with propriety of expression.

Methods:

  • Final oral exam
  • Final written exam
  • Periodic written tests

Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • preparation of oral/written report

Attendance: Advised

Teaching methods:

  • Lectures

Syllabus
First part: commutative algebra: integral extensions of rings, dimension theory of local noetherian rings, completions,relations with algebraic geometry; Second part: homological algebra: injective modules, projective modules, extensions, some notions on categories, functors, derived functors (examples of Tor^n and Ext^n), cohomology of groups with local coefficients.
Bibliography
Recommended reading includes the following works: Atiyah-MacDonald, Introduction to Commutative Algebra, Hilton-Stammbach, Homological Algebra. Further bibliography will be indicated.
Ultimo aggiornamento 14/11/2016 17:27