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
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.
Oral.
