Moderately ramified actions in positive characteristic

In characteristic 2 and dimension 2, wild Z / 2 Z -actions on k [[ u ,  v ]] ramified precisely at the origin were classified by Artin, who showed in particular that they induce hypersurface singularities. We introduce in this article a new class of wild quotient singularities in any characteristic...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2020-08, Vol.295 (3-4), p.1095-1142
Main Authors: Lorenzini, Dino, Schröer, Stefan
Format: Article
Language:English
Subjects:
Hyperspaces
Invariants
Mathematics
Mathematics and Statistics
Power series
Quotients
Singularity (mathematics)
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Summary:In characteristic 2 and dimension 2, wild Z / 2 Z -actions on k [[ u ,  v ]] ramified precisely at the origin were classified by Artin, who showed in particular that they induce hypersurface singularities. We introduce in this article a new class of wild quotient singularities in any characteristic p > 0 and dimension n ≥ 2 arising from certain non-linear actions of Z / p Z on the formal power series ring k [ [ u 1 , ⋯ , u n ] ] . These actions are ramified precisely at the origin, and their rings of invariants in dimension 2 are hypersurface singularities, with an equation of a form similar to the form found by Artin when p = 2 . In higher dimension, the rings of invariants are not local complete intersection in general, but remain quasi-Gorenstein. We establish several structure results for such actions and their corresponding rings of invariants.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-019-02408-4