Abstract
Let k be an arbitrary field and X be a reduced k-scheme of finite type. Let \(\gamma \) be an arc on X, not entirely contained in the non-smooth locus of X. We show that the nilpotents in the local ring at \(\gamma \) vanish in the completion. Along the way, we also obtain informations on the connection between torsion differential forms and nilpotent functions on arc schemes in positive characteristic.
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Bourqui, D., Haiech, M. On the nilpotent functions at a non-degenerate arc. manuscripta math. 165, 227–238 (2021). https://doi.org/10.1007/s00229-020-01209-y
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DOI: https://doi.org/10.1007/s00229-020-01209-y