no. 5
Homological algebra/Algebraic geometry
Algebraic K-theory with coefficients of cyclic quotient singularities

Présenté par : Michel Duflo

Tabuada, Gonçalo1, 2, 3
1 Department of Mathematics, MIT, Cambridge, MA 02139, USA
2 Departamento de Matemática, FCT, UNL, Portugal
3 Centro de Matemática e Aplicações (CMA), FCT, UNL, Portugal
Comptes Rendus. Mathématique, Tome 354 (2016) no. 5, pp. 449-452.

Dans cette note, en combinant les travaux de Amiot–Iyama–Reiten et Thanhoffer de Völcsey–Van den Bergh sur les modules Cohen–Macaulay avec le travail précédent de l'auteur sur les catégories d'orbites, nous calculons la K-théorie algébrique avec coefficients des singularités quotient cycliques.

In this note, by combining the work of Amiot–Iyama–Reiten and Thanhoffer de Völcsey–Van den Bergh on Cohen–Macaulay modules with the previous work of the author on orbit categories, we compute the algebraic K-theory with coefficients of cyclic quotient singularities.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.01.017
Tabuada, Gonçalo 1, 2, 3

1 Department of Mathematics, MIT, Cambridge, MA 02139, USA
2 Departamento de Matemática, FCT, UNL, Portugal
3 Centro de Matemática e Aplicações (CMA), FCT, UNL, Portugal 
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Tabuada, Gonçalo. Algebraic K-theory with coefficients of cyclic quotient singularities. Comptes Rendus. Mathématique, Tome 354 (2016) no. 5, pp. 449-452. doi : 10.1016/j.crma.2016.01.017. http://www.numdam.org/articles/10.1016/j.crma.2016.01.017/

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[2] de Thanhoffer, L.; Van den Bergh, M. Explicit models for some stable categories of maximal Cohen–Macaulay modules, 2016 (Math. Res. Lett., in press) | arXiv

[3] Keller, B. On triangulated orbit categories, Doc. Math., Volume 10 (2005), pp. 551-581

[4] Orlov, D. Triangulated categories of singularities and D-branes in Landau–Ginzburg models, Proc. Steklov Inst. Math., Volume 246 (2004), pp. 227-248

[5] Orlov, D. Derived categories of coherent sheaves and triangulated categories of singularities, Algebra, Arithmetic, and Geometry: In Honor of Yu.I. Manin, vol. II, Progr. Math., vol. 270, Birkhäuser Boston, Inc., Boston, MA, USA, 2009, pp. 503-531

[6] Suslin, A. On the K-theory of local fields, J. Pure Appl. Algebra, Volume 34 (1984) no. 2–3, pp. 301-318 (in: Proceedings of the Luminy Conference on Algebraic K-Theory, Luminy, 1983)

[7] Tabuada, G. A1-homotopy invariants of dg orbit categories, J. Algebra, Volume 434 (2015), pp. 169-192

[8] Tabuada, G. A1-homotopy invariance of algebraic K-theory with coefficients and Kleinian singularities, 2016 (Annals of K-theory, in press) | arXiv

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