On the Grinberg - Kazhdan formal arc theorem

By V. Drinfeld. 2002

46 citations recorded by the source corpus.

Let X be an algebraic variety over a field k, and L(X) be the scheme of formal arcs in X. Let f be an arc whose image is not contained in the singularities of X. Grinberg and Kazhdan proved that if k has characteristic 0 then the formal neighborhood of f in L(X) admits a decomposition into a product of an infinite-dimensional smooth piece and a piece isomorphic to the formal neighborhood of a closed point of a scheme of finite type. We give a short proof of this theorem without the characteristic 0 assumption.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7a4d7530a498793820a9d49717ba0f12d66d4ce2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Weyl modules and $$q$$q-Whittaker functions (2012, background): “According to [6,17], the formal completion of Q at a closed point x ∈ Q is isomorphic to the product of the formal completion of a certain QMg at a closed point φ ∈ QMg, and countably many copies of the formal disc.”
On the formal arc space of a reductive monoid (2014, methodology): “According to Grinberg, Kazhdan [12] and Drinfeld [9] it is known, nevertheless, that the singularity of L X at a non-degenerate arc is ﬁnite dimensional, i.e., for every non-degenerate arc x ∈ L X , the formal completion of L X at x is isomorphic to Y y × D ∞ where Y y is the formal completion of a…”