论文信息 - Notes on G-theory of Deligne-Mumford stacks

Notes on G-theory of Deligne-Mumford stacks

Based on the methods used by the author to prove the Riemann-Roch formula for algebraic stacks, this paper contains a description of the rationnal G-theory of Deligne-Mumford stacks over general bases. We will use these results to study equivariant K-theory, and also to define new filtrations on K-theory of algebraic stacks.

B. Toen

[1] G. Vezzosi,et al. Higher algebraic K-theory of group actions with finite stabilizers , 1999, math/9912155.

[2] Bertrand Toën. Théorèmes de Riemann-Roch pour les champs de Deligne-Mumford , 1999 .

[3] Bertrand Toën. K-théorie et cohomologie des champs algébriques. , 1999 .

[4] D. Edidin. On quotient stacks , 1999 .

[5] Angelo Vistoli. Equivariant Grothendieck groups and equivariant Chow groups , 1992 .

[6] D. M. Kan,et al. Homotopy Limits, Completions and Localizations , 1987 .

[7] R. Thomason. Lefschetz-Riemann-Roch theorem and coherent trace formula , 1986 .

[8] C. Soulé. Opérations En K-Théorie Algébrique , 1985, Canadian Journal of Mathematics.

[9] H. Gillet. Homological descent for the K-theory of coherent sheaves , 1984 .

[10] C. Soulé,et al. Filtrations On Higher Algebraic K-Theory , 1983 .

[11] P. Deligne,et al. Théorie de Hodge, II , 1971 .

[12] A. Grothendieck,et al. Groupes de Type Multiplicatif, et Structure des Schémas en Groupes Généraux , 1970 .