Dans cette Note, nous montrons que tout champ algébrique dont l'inertie est finie, est étale-localement isomorphe au quotient d'un schéma affine par une action du groupe général linéaire.
In this Note we show that an Artin stack with finite inertia stack is étale locally isormorphic to the quotient of an affine scheme by an action of a general linear group.
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@article{CRMATH_2010__348_19-20_1107_0, author = {Iwanari, Isamu}, title = {Note on local structure of {Artin} stacks}, journal = {Comptes Rendus. Math\'ematique}, pages = {1107--1109}, publisher = {Elsevier}, volume = {348}, number = {19-20}, year = {2010}, doi = {10.1016/j.crma.2010.09.022}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.09.022/} }
TY - JOUR AU - Iwanari, Isamu TI - Note on local structure of Artin stacks JO - Comptes Rendus. Mathématique PY - 2010 SP - 1107 EP - 1109 VL - 348 IS - 19-20 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.09.022/ DO - 10.1016/j.crma.2010.09.022 LA - en ID - CRMATH_2010__348_19-20_1107_0 ER -
Iwanari, Isamu. Note on local structure of Artin stacks. Comptes Rendus. Mathématique, Tome 348 (2010) no. 19-20, pp. 1107-1109. doi : 10.1016/j.crma.2010.09.022. http://archive.numdam.org/articles/10.1016/j.crma.2010.09.022/
[1] Compactifying the space of stable maps, J. Amer. Math. Soc., Volume 15 (2005), pp. 27-75
[2] Tame stacks in positive characteristic, Ann. Inst. Fourier (Grenoble), Volume 58 (2008), pp. 1057-1091
[3] B. Conrad, The Keel–Mori theorem via stacks, preprint.
[4] Brauer groups and quotient stacks, Amer. J. Math., Volume 123 (2001), pp. 761-777
[5] Stable points on algebraic stacks, Adv. Math., Volume 223 (2010), pp. 257-299
[6] Riemann–Roch for algebraic stacks: I, Compositio Math., Volume 136 (2003), pp. 117-169
[7] Quotients by groupoids, Ann. of Math., Volume 145 (1997), pp. 193-213
[8] Algebraic Spaces, Lecture Notes in Math., vol. 203, Springer, 1971
[9] Champs Algébriques, Springer-Verlag, 2000
[10] S. Mitchell, Hypercohomology spectra and Thomason's descent theorem, preprint.
[11] Hom-stacks and restriction of scalars, Duke Math. J., Volume 134 (2006), pp. 139-164
[12] Algebraic K-theory and étale cohomology, Ann. Sci. Ec. Norm. Sup., Volume 18 (1985), pp. 437-552
[13] Algebraic K-theory of group scheme actions (Browder, W., ed.), Algebraic Topology and Algebraic K-theory, Ann. Math. Stud., vol. 113, Princeton University Press, Princeton, NJ, 1987, pp. 539-563
[14] Equivariant resolution, linearization, and Hilbert's fourteenth problem over arbitrary base schemes, Adv. Math., Volume 65 (1987), pp. 16-34
[15] Equivariant algebraic vs. topological K-homology Atiyah–Segal-style, Duke Math. J., Volume 56 (1988), pp. 589-636
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