Credits: 9

Type: advanced

Objectives:

In this unit students will examine the the concepts, results and techniques employed in local algebra in order to understand the local properties used in various areas of algebra, combinatorics and geometry.

Knowledge:

• Completion.
• Tor and Ext functors.
• Homological dimensions. The syzygies theorem .
• Regular succession and the theory of degree.
• Cohen-Macaulay rings and modules.
• Hilbert functions and multiplicities.

Subject-specific competences:

• To show understanding of the process of completion in an algebraic context and of Hensel's lemma.
• To be able to obtain the resolution of ideals and modules and their numerical invariants.
• To be able to calculate and apply Hilbert functions.