Nilpotency in arc schemes
Since Nash, we know that the associated arc scheme
can be used in the study of the singularities of the involved variety. Various works
of Mustata and Drinfeld suggest that the nilpotency at the level of arc schemes could
carry a part of this information. We will give different evidences in this direction.
(A part of this talk is based on a joint work with David Bourqui.)