46 citations · 65 across the 6 of their papers we have counts for
7 papers
On the behavior of formal neighborhoods in the Nash sets associated with toric valuations: a comparison theorem
David Bourqui, Mario Morán Cañón, Julien Sebag
We show that there exists a strong connection between the generic formal neighborhood at a rational arc lying in the Nash set associated with a toric divisorial valuation on a tori…
A question of Joseph Ritt from the point of view of vertex algebras
Tomoyuki Arakawa, Kazuya Kawasetsu, Julien Sebag
Let be a field of characteristic zero. This paper studies a problem proposed by Joseph F. Ritt in 1950. Precisely, we prove that (1) If is an integer, for every integ…
Birational self-maps and piecewise algebraic geometry
Stéphane Lamy, Julien Sebag
Let X be a smooth projective complex variety, of dimension 3, whose Hodge numbers h^{3,0}(X), h^{1,0}(X) both vanish. Let f: X--> X be a birational map that induces an isomorphism…
A note on motivic integration in mixed characteristic
Johannes Nicaise, Julien Sebag
We introduce a quotient of the Grothendieck ring of varieties by identifying classes of universally homeomorphic varieties. We show that the standard realization morphisms factor t…
Greenberg approximation and the geometry of arc spaces
Johannes Nicaise, Julien Sebag
We study the differential properties of generalized arc schemes, and geometric versions of Kolchin's Irreducibility Theorem over arbitrary base fields. As an intermediate step, we…
Motivic Serre invariants, ramification, and the analytic Milnor fiber
Johannes Nicaise, Julien Sebag
We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We i…
Motivic integration on smooth rigid varieties and invariants of degenerations
F. Loeser, J. Sebag
We construct a theory of motivic integration for smooth rigid varieties. As an application new invariants of degenerations are obtained.