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 polynomiality of the invariant ring and principality of the plinth ideal. We also present some conjectures and open problems.

doi: 10.1007/s00031-022-09764-2

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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