Mathematics Department

Virtual Commutative algebra seminar

Speaker: Shigeru Kuroda, Tokyo Metropolitan University, Hachioji, Japan
Date/Time: Friday, 23 December 2022, 5:30pm 

Gmeet link: meet.google.com/wph-nyzd-hyj

Title: Z/pZ-actions on the affine space: classification, invariant ring, and plinth ideal 

Abstract: Let k be a field of characteristic p>0. In this talk, we consider the Z/pZ-actions on the affine n-space over k, or equivalently the order p automorphisms of the polynomial ring k[X] in n variables over k. For example, every automorphism induced from a G_a-action is of order p. Hence, the famous automorphism of Nagata is of order p. Such an automorphism is important to study the automorphism group of the k-algebra k[X].

We discuss two topics: (1) classification, and (2) the relation between the polynomiality of the invariant ring and the principality of the plinth ideal. We also present some conjectures and open problems.

For more information and links to previous seminars, visit the website of VCAS: 

https://sites.google.com/view/virtual-comm-algebra-seminar