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Some remarks about the Dedekind-Mertens lemma

Jakub Byszewski — 2016

Banach Center Publications

The Dedekind-Mertens lemma relates the contents of two polynomials and the content of their product. Recently, Epstein and Shapiro extended this lemma to the case of power series. We review the problem with a special emphasis on the case of power series, give an answer to a question posed by Epstein-Shapiro and investigate extensions of some related results. This note is of expository character and discusses the history of the problem, some examples and announces some new results.

Which weakly ramified group actions admit a universal formal deformation?

Jakub Byszewski; Gunther Cornelissen — 2009

Annales de l’institut Fourier

Consider a representation of a finite group $G$ as automorphisms of a power series ring $k [[t]]$ over a perfect field $k$ of positive characteristic. Let $D$ be the associated formal mixed-characteristic deformation functor. Assume that the action of $G$ is weakly ramified, i.e., the second ramification group is trivial. Example: for a group action on an ordinary curve, the action of a ramification group on the completed local ring of any point is weakly ramified. We prove...

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