University of Birmingham > Talks@bham > Algebra Seminar > Modular invariant theory and Galois ring extensions

Modular invariant theory and Galois ring extensions

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If you have a question about this talk, please contact David Craven.

This is joint work with C.F. Woodcock (Kent). We investigate trace surjective commutative G-algebras in characteristic p>0, defined by non-linear actions of finite p-groups. These arise in the analysis of dehomogenized modular invariant rings and related localizations. We describe criteria for such a dehomogenized invariant ring to be a polynomial ring or stably polynomial. Among other things it turns out that every finite p-group has a faithful (non-linear) representation on a polynomial ring with invariant ring being again a polynomial ring. This is in contrast to homogeneous linear actions, where, due to a result of Serre, the graded invariants can only form a polynomial ring, if G is generated by pseudo-reflections.

This talk is part of the Algebra Seminar series.

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