|SCIENTIFIC DISCIPLINARY SECTOR||MAT/02|
|LANGUAGE||Italian (English on demand)|
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
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 style: In presence
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.
The class will start according to the academic calendar.
All class schedules are posted on the EasyAcademy portal.