The Drinfeld-Grinberg-Kazhdan Theorem for formal schemes and singularity theory
Confluentes Mathematici, Tome 9 (2017) no. 1, pp. 29-64.

Let k be a field. In this article, we provide an extended version of the Drinfeld-Grinberg-Kazhdan Theorem in the context of formal geometry. We prove that, for every formal scheme V topologically of finite type over Spf(k[[T]]), for every non-singular arc γ (V)(k), there exists an affine noetherian adic formal k-scheme 𝒮 and an isomorphism of formal k-schemes

(V)γ𝒮×kSpf(k[[(Ti)iN]]).

We emphasize the fact that the proof is constructive and, when V is the completion of an affine algebraic k-variety, effectively implementable. Besides, we derive some properties of such an isomorphism in the direction of singularity theory.

Reçu le : 2015-12-17
Accepté le : 2016-10-13
Accepté après révision le : 2016-12-10
Publié le : 2017-09-14
DOI : https://doi.org/10.5802/cml.35
Classification : 14E18,  14B05
Mots clés: Arc scheme, formal neighborhood
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     author = {David Bourqui and Julien Sebag},
     title = {The Drinfeld-Grinberg-Kazhdan Theorem for formal schemes and singularity theory},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {9},
     number = {1},
     year = {2017},
     pages = {29-64},
     doi = {10.5802/cml.35},
     language = {en},
     url = {cml.centre-mersenne.org/item/CML_2017__9_1_29_0/}
}
Bourqui, David; Sebag, Julien. The Drinfeld-Grinberg-Kazhdan Theorem for formal schemes and singularity theory. Confluentes Mathematici, Tome 9 (2017) no. 1, pp. 29-64. doi : 10.5802/cml.35. https://cml.centre-mersenne.org/item/CML_2017__9_1_29_0/

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