The Grothendieck-Riemann-Roch theorem for group scheme actions

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1. [At] M. F. ATIYAH, Characters and cohomology of finite groups (Publ. Math. IHES, Vol. 9, 1961, pp. 23-64). Zbl0107.02303MR26 #6228
2. [AT] M. F. ATIYAH and D. O. TALL, Group representations, λ-rings and the J-homomorphism (Topology, Vol. 8, 1969, pp. 253-297). Zbl0159.53301MR39 #5702
3. [Ba] H. BASS, Algebraic K-theory (Math. Lecture Note Series, Benjamin, New York, 1968). Zbl0174.30302MR40 #2736
4. [SGA6] P. BERTHELOT, A. GROTHENDIECK and L. ILLUSIE, Théorie des Intersections et Théorème de Riemann-Roch (Lecture Notes in Math., Vol. 225, Springer, New York, 1971). Zbl0218.14001MR50 #7133
5. [Bo] R. BOLTJE, Mackey functors and related structures in representation theory and number theory, Report No. 327, Institut für Mathematik der Universität Augsburg, 1995. 
6. [BV] M. BRION and M. VERGNE, An equivariant Riemann-Roch theorem for complete, simplicial toric varieties (J. Reine Angew. Math., Vol. 482, 1997, pp. 67-92). Zbl0862.14006MR98a:14067
7. [BC] D. BURNS and T. CHINBURG, Adams operations and integral Hermitian-Galois representations (Amer. J. Math., Vol. 118, 1996, pp. 925-962). Zbl0865.11076MR98g:11126
8. [CNT] Ph. CASSOU-NOGUÈS and M. J. TAYLOR, Opérations d'Adams et Groupe des classes d'Algèbre de groupe (J. Algebra, Vol. 95, 1985, pp. 125-152). Zbl0603.12007MR87a:11116
9. [CEPT] T. CHINBURG, B. EREZ, G. PAPPAS and M. J. TAYLOR, Riemann-Roch type theorems for arithmetic schemes with a finite group action (J. Reine Angew. Math., Vol. 489, 1997, pp. 151-187). Zbl0903.19001MR98e:14006
10. [CR] C. W. CURTIS and I. REINER, Methods of representation theory with applications to finite groups and orders I (Pure Appl. Math., Wiley, New York, 1981). Zbl0469.20001
11. [De] M. DEMAZURE, Désingularisation des variétés de Schubert généralisées (Ann. Sci. École Norm. Sup., (4), Vol. 7, 1974, pp. 53-88). Zbl0312.14009MR50 #7174
12. [SGA3] M. DEMAZURE and A. GROTHENDIECK, Schémas en Groupes I, II, III (Lecture Notes in Math., Vol. 151-152-153, Springer, New York, 1970). MR43 #223a
13. [EG] D. EDIDIN and W. GRAHAM, Equivariant intersection theory, preprint, alg-geom/9603008. 
14. [FH] W. FULTON and J. HARRIS, Representation theory (Grad. Texts in Math., Vol. 129, Springer, New York, 1991). Zbl0744.22001MR93a:20069
15. [FL] W. FULTON and S. LANG, Riemann-Roch algebra (Grundlehren Math. Wiss., Vol. 277, Springer, New York, 1985). Zbl0579.14011MR88h:14011
16. [FM] W. FULTON and R. MACPHERSON, Characteristic classes of direct image bundles for covering maps (Ann. of Math., Vol. 125, 1987, pp. 1-92). Zbl0628.55010MR88f:14015
17. [Gr] D. R. GRAYSON, Exterior power operations on higher K-theory (K-theory, Vol. 3, 1989, pp. 247-260). Zbl0701.18007MR91h:19005
18. [Gro1] A. GROTHENDIECK, Sur quelques propriétés fondamentales en théorie des intersections, Séminaire C. Chevalley, 2e année, Anneaux de Chow et applications, Secr. Math. Paris, 1958. MR21 #5637
19. [Gro2] A. GROTHENDIECK, Classes de Chern et représentations linéaires des groupes discrets, in J. Giraud et al., Dix exposés sur la cohomologie des schémas (Adv. Stud. Pure Math., North-Holland Publishing Company, Amsterdam, 1968, pp. 215-305). Zbl0198.26101MR42 #280
20. [EGA] A. GROTHENDIECK and J. A. DIEUDONNÉ, Eléments de Géométrie Algébrique I (Grundlehren Math. Wiss., Vol. 166, Springer, New York, 1971) ; ...II, III, (Publ. Math. IHES, Vol. 8, 1961, Vol. 11, 1961, Vol. 17, 1963). 
21. [Ha] R. HARTSHORNE, Algebraic geometry (Graduate Texts in Math., Vol. 52, Springer, New York, 1977). Zbl0367.14001MR57 #3116
22. [Hi] H. L. HILLER, λ-rings and algebraic K-theory (J. Pure Appl. Algebra, Vol. 20, 1981, pp. 241-266). Zbl0471.18007MR82e:18016
23. [J] J. C. JANTZEN, Representations of algebraic groups (Pure Appl. Math., Vol. 131, Academic Press, Boston, 1987). Zbl0654.20039MR89c:20001
24. [Ke] M. KERVAIRE, Opérations d'Adams en Théorie des représentations linéaires des groupes finis (Enseign. Math., Vol. 22, 1976, pp. 1-28). Zbl0335.20003MR54 #5325
25. [Ko0] B. KÖCK, Das Lefschetz- und Riemann-Roch-Theorem in der höheren äquivarianten K-Theorie Dissertation, Regensburg, 1989. 
26. [Ko1] B. KÖCK, Chow motif and higher Chow theory of G / P (Manuscripta Math., Vol. 70, 1991, pp. 363-372). Zbl0735.14001MR91m:14077
27. [Ko2] B. KÖCK, Das Adams-Riemann-Roch-Theorem in der höheren äquivarianten K-Theorie (J. Reine Angew. Math., Vol. 421, 1991, pp. 189-217). Zbl0731.19005
28. [Ko3] B. KÖCK, The Lefschetz theorem in higher equivariant K-theory (Comm. Algebra, Vol. 19, 1991, pp. 3411-3422). Zbl0760.14004MR93g:19008
29. [Ko4] B. KÖCK, Higher K'-groups of integral group rings (K-Theory, Vol. 4, 1991, pp. 177-187). Zbl0752.16013MR93a:19002
30. [Ko5] B. KÖCK, Shuffle products in higher K-theory (J. Pure Appl. Algebra, Vol. 92, 1994, pp. 269-307). Zbl0797.19003MR95c:19001
31. [Ko6] B. KÖCK, The Grothendieck-Riemann-Roch theorem in the higher K-theory of group scheme actions Habilitationsschrift, Karlsruhe, 1995. 
32. [Ko7] B. KÖCK, On Adams operations on the higher K-theory of group rings, in : G. Banaszak et al. (eds.), Algebraic K-theory (Poznań, 1995) (Contemp. Math., Vol. 199, Amer. Math. Soc., Providence, 1996, pp. 139-150). Zbl0857.19001
33. [Ko8] B. KÖCK, Adams operations for projective modules over group rings (Math. Proc. Cambridge Philos. Soc., Vol. 122, 1997, pp. 55-71). Zbl0884.19002MR98g:13013
34. [Ko9] B. KÖCK, Operations on locally free classgroups, preprint, Karlsruhe, 1997. 
35. [Ko10] B. KÖCK, Riemann-Roch for tensor power, preprint, Karlsruhe, 1998. 
36. [KK1] B. KOSTANT and S. KUMAR, The nil Hecke ring and cohomology of G/P for a Kac-Moody group G (Adv. Math., Vol. 62, 1986, pp. 187-237). Zbl0641.17008MR88b:17025b
37. [KK2] B. KOSTANT and S. KUMAR, T-equivariant K-theory of generalized flag varieties (J. Differential Geom., Vol. 32, 1990, pp. 549-603). Zbl0731.55005MR92c:19006
38. [Kr] Ch. KRATZER, λ-Structure en K-théorie algébrique (Comment. Math. Helv., Vol. 55, 1980, pp. 233-254). Zbl0444.18008
39. [La] A. LASCOUX, Anneau de Grothendieck de la variété de drapeaux, in The Grothendieck Festschrift, vol. III (Progr. Math., Vol. 88, Birkhäuser, Boston, 1990, pp. 1-34). Zbl0742.14041MR92j:14064
40. [Le] H. W. LENSTRA, Grothendieck groups of abelian group rings (J. Pure Appl. Algebra, Vol. 20, 1981, pp. 173-193). Zbl0467.16016MR82g:16024
41. [Man] Y. I. MANIN, Lectures on the K-functor in algebraic geometry (Russian Math. Surveys, Vol. 24, No. 5, 1969, pp. 1-89). Zbl0204.21302MR42 #265
42. [Mo] R. MORELLI, The K theory of a toric variety (Adv. Math., Vol. 100, 1993, pp. 154-182). Zbl0805.14025MR94j:14047
43. [Mum] D. MUMFORD, Geometric invariant theory (Ergeb. Math. Grenzgeb., Vol. 34, Springer, New York, 1965). Zbl0147.39304MR35 #5451
44. [Q] D. QUILLEN, Higher algebraic K-theory : I, in H. Bass (ed.), Algebraic K-Theory I (Seattle, 1972) (Lecture Notes in Math., Vol. 341, Springer, New York, 1973, pp. 85-147). Zbl0292.18004MR49 #2895
45. [Sn] V. P. SNAITH, Invariants of representations, in J. F. Jardine and V. P. Snaith (eds.), Algebraic K-theory : Connections with geometry and topology (Lake Louise, 1987) (NATO Adv. Sci. Inst. Ser. C : Math. Phys. Sci., Vol. 279, Kluwer Acad. Publ., Dordrecht, 1989, pp. 445-508). Zbl0721.20004MR91h:20010
46. [So] C. SOULÉ, Opérations en K-Théorie algébrique (Canad. J. Math., Vol. 37, No. 3, 1985, pp. 488-550). Zbl0575.14015MR87b:18013
47. [Su] H. SUMIHIRO, Equivariant completion II (J. Math. Kyoto Univ., Vol. 15, 1975, pp. 573-605). Zbl0331.14008MR52 #8137
48. [Ta] G. TAMME, The theorem of Riemann-Roch, in M. Rapoport, N. Schappacher and P. Schneider (eds.), Beilinson's conjectures on special values of L-functions (Perspect. in Math., Vol. 4, Academic Press, Boston, 1988, pp. 103-168). Zbl0664.14004MR89d:14013
49. [Tho] C. B. THOMAS, Characteristic classes and the cohomology of finite groups (Cambridge Stud. Adv. Math., Vol. 9, Cambridge Univ. Press, Cambridge, 1986). Zbl0618.20036MR88f:20005
50. [Th1] R. W. THOMASON, Absolute cohomological purity (Bull. Soc. Math. France, Vol. 112, 1984, pp. 397-406). Zbl0584.14007MR87e:14018
51. [Th2] R. W. THOMASON, Lefschetz-Riemann-Roch theorem and coherent trace formula (Invent. Math., Vol. 85, 1986, pp. 515-543). Zbl0653.14005MR87j:14028
52. [Th3] R. W. THOMASON, Algebraic K-theory of group scheme actions, in W. Browder (ed.), Algebraic topology and algebraic K-theory (Princeton, 1983) (Ann. Math. Stud., Vol. 113, Univ. Press, Princeton, 1987, pp. 539-563). Zbl0701.19002MR89c:18016
53. [Th4] R. W. THOMASON, Une formule de Lefschetz en K-théorie équivariante algébrique (Duke Math. J., Vol. 68, 1992, pp. 447-462). Zbl0813.19002MR93m:19007
54. [Th5] R. W. THOMASON, Les K-groupes d'un schéma éclaté et une formule d'intersection excédentaire (Invent., Math., Vol. 112, 1993, pp. 195-215). Zbl0816.19004MR93k:19005
55. [We] C. A. WEIBEL, Homotopy algebraic K-theory, in M. R. Stein and R. K. Dennis (eds.), Algebraic K-theory and algebraic number theory (Honolulu, 1987) (Contemp. Math., Vol. 83, Amer. Math. Soc., Providence, 1989, pp. 461-488). Zbl0669.18007MR90d:18006

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