Duke Mathematical Journal

Cycle classes and Riemann-Roch for crystalline cohomology

Henri Gillet and William Messing

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 55, Number 3 (1987), 501-538.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077306163

Digital Object Identifier
doi:10.1215/S0012-7094-87-05527-X

Mathematical Reviews number (MathSciNet)
MR904940

Zentralblatt MATH identifier
0651.14014

Subjects
Primary: 14F30: $p$-adic cohomology, crystalline cohomology
Secondary: 14C15: (Equivariant) Chow groups and rings; motives 14C40: Riemann-Roch theorems [See also 19E20, 19L10] 14F12

Citation

Gillet, Henri; Messing, William. Cycle classes and Riemann-Roch for crystalline cohomology. Duke Math. J. 55 (1987), no. 3, 501--538. doi:10.1215/S0012-7094-87-05527-X. https://projecteuclid.org/euclid.dmj/1077306163


Export citation

References

  • [CC] P. Berthelot, Cohomologie cristalline des schémas de caractéristique $p>0$, Lecture Notes in Math., vol. 407, Springer-Verlag, Berlin, 1974.
  • [EGA]1 A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. I, Inst. Hautes Études Sci. Publ. Math. (1964), no. 20, 259.
  • [EGA]2 A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math. (1965), no. 24, 231.
  • [EGA]3 A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. III, Inst. Hautes Études Sci. Publ. Math. (1966), no. 28, 255.
  • [EGA]4 A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV, Inst. Hautes Études Sci. Publ. Math. (1967), no. 32, 361.
  • [SGA4 1/2] P. Deligne, Séminaire de géométrie algébrique: Cohomologie étale, Lecture Notes in Math., vol. 569, Springer-Verlag, Berlin, 1977.
  • [SGA6] P. Berthelot, A. Grothendieck, and L. Illusie, Séminaire de géométrie algébrique: Théorie des intersections et théorème de Riemann-Roch, Lecture Notes in Math., vol. 225, Springer-Verlag, Berlin, 1971.
  • [BFM] P. Baum, W. Fulton, and R. MacPherson, Riemann-Roch for singular varieties, Inst. Hautes Études Sci. Publ. Math. (1975), no. 45, 101–145.
  • [B--I] P. Berthelot and L. Illusie, Classes de Chern en cohomologie cristalline, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1695-A1697; ibid. 270 (1970), A1750–A1752.
  • [B--M] P. Berthelot and W. Messing, Théorie de Dieudonné cristalline III, to appear.
  • [B--M2] P. Berthelot and W. Messing, Théorie de Dieudonné cristalline. I, Journées de Géométrie Algébrique de Rennes (Rennes, 1978), Vol. I, Astérisque, vol. 63, Soc. Math. France, Paris, 1979, pp. 17–37.
  • [B--O1] P. Berthelot and A. Ogus, Notes on crystalline cohomology, Mathematical Notes, vol. 21, Princeton Univ. Press, Princeton, N.J., 1978.
  • [B--O2] P. Berthelot and A. Ogus, $F$-isocrystals and de Rham cohomology. I, Invent. Math. 72 (1983), no. 2, 159–199.
  • [E] R. Elkik, L'équivalence rationnelle, Séminaire de géométrie analytique (École Norm. Sup., Paris, 1974–75), Astérique, vol. 36-37, Suc. Math. France, Paris, 1976, pp. 35–63.
  • [Fon1] J-M. Fontaine, Modules galoisiens, modules filtrés et anneaux de Barsotti-Tate, Journées de géométrie algébrique de Rennes. (Rennes, 1978), Vol. III, Astérisque, vol. 65, Soc. Math. France, Paris, 1979, pp. 3–80.
  • [Fon2] J-M. Fontaine, Sur certains types de représentations $p$-adiques du groupe de Galois d'un corps local; construction d'un anneau de Barsotti-Tate, Ann. of Math. (2) 115 (1982), no. 3, 529–577.
  • [Fon.-Mess] J.-M. Fontaine and W. Messing, Constructing $p$-adic étale cohomology, in preparation.
  • [F] W. Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984.
  • [F--M] W. Fulton and R. MacPherson, Intersecting cycles on an algebraic variety, Real and Complex Singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 179–197.
  • [G1] H. Gillet, The applications of $K$-theory to intersection theory, Thesis, Harvard University, 1978.
  • [G2] H. Gillet, Riemann-Roch theorems for higher algebraic $K$-theory, Adv. in Math. 40 (1981), no. 3, 203–289.
  • [G3] H. Gillet, Comparison of $K$-theory spectral sequences, with applications, Algebraic $K$-theory, Evanston, 1980 (Proc. Conf., Northwestern Univ., Evanston, Ill., 1980), Lecture Notes in Math., vol. 854, Springer-Vrelag, Berlin, 1981, pp. 141–167.
  • [G4] H. Gillet, Universal cycle classes, Compositio Math. 49 (1983), no. 1, 3–49.
  • [G5] H. Gillet, $K$-theory and intersection theory revisited, to appear.
  • [Gra] D. Grayson, Products in $K$-theory and intersecting algebraic cycles, Invent. Math. 47 (1978), no. 1, 71–83.
  • [Gro] M. Gros, Classes de Chern et classes de cycles en cohomologie logarithmique, Orsay, 1983, thèse de $3^\circ$ cycle.
  • [Groth.1] A. Grothendieck, Sur quelques propriétés fondamentales en théorie des intersections, Sém. C. Chevalley 2^e annee, Anneaux de Chow et applications, Secr. Math., Paris, 1958.
  • [Groth.2] A. Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France 86 (1958), 137–154.
  • [H] R. Hartshorne, On the De Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. (1975), no. 45, 5–99.
  • [K1] S. Kleiman, Algebraic cycles and the Weil conjectures, Dix esposés sur la cohomologie de schémas, North Holland, Amsterdam, 1968, pp. 359–386.
  • [N] M. Nagata, Imbedding of an abstract variety in a complete variety, J. Math. Kyoto Univ. 2 (1962), 1–10.
  • [Q] D. Quillen, Higher algebraic $K$-theory 1, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin, 1973, pp. 85–147.
  • [R] J. Roberts, Chow's moving lemma, Algebraic Geometry, Oslo, 1970 (Proc. Fifth Nordic Summer School in Math.), Wolters-Noordhoff Publ., Groningen, 1972, pp. 89–96.
  • [S] C. Soulé, Operations en $K$-theorie algébrique, preprint, 1983.