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COMMUTATIVE ALGEBRA 2

CODE 42911
ACADEMIC YEAR 2022/2023
CREDITS
  • 7 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA
  • 6 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/02
    LANGUAGE Italian (English on demand)
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 2° Semester
    TEACHING MATERIALS AULAWEB

    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

    LESSONS

    LESSONS START

    The class will start according to the academic calendar.

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    Oral.