HIGHER ALGEBRA 2

HIGHER ALGEBRA 2

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Code
42911
ACADEMIC YEAR
2019/2020
CREDITS
7 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/02
LANGUAGE
Italian (English on demand)
TEACHING LOCATION
GENOVA (Mathematics)
semester
2° Semester
Teaching materials

OVERVIEW

Language: Italian

This is a course on Commutative Algebra, and will be centered on the issue of the lack of bases for modules over a ring: most modules are not free, so one has to "approximate" them in some way. The better is the approximation, the better is the ring, in a sense that agrees with the geometric concept of singularities: we will see in detail regular ring, Cohen-Macaulay rings, UFD's, techniques from homological algebra

AIMS AND CONTENT

LEARNING OUTCOMES

Provide students with the basics of homologous algebra and notions such as free resolution and depth of a module; Introduce / deepen regular rings, Cohen-Macaulai rings, and UFDs.

Teaching methods

Teaching style: In presence

SYLLABUS/CONTENT

Homological algebra. Hilbert functions. Regular sequences. Grade and depth. The Koszul complex. Free resolutions. Regular rings. Cohen-Macaulay rings. Complete intersections. Gorenstein rings. Canonical modules and local cohomology. Stanley Reisner rings, determinanntal rings. 

TEACHERS AND EXAM BOARD

Exam Board

MATTEO VARBARO (President)

MARIA EVELINA ROSSI

EMANUELA DE NEGRI

LESSONS

Teaching methods

Teaching style: In presence

LESSONS START

The class will start according to the academic calendar.

EXAMS

Exam description

Oral.