Kodai Mathematical Journal

Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over ${\bf C}$

Kazuya Kato and Chikara Nakayama

Full-text: Open access

Article information

Source
Kodai Math. J. Volume 22, Number 2 (1999), 161-186.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
http://projecteuclid.org/euclid.kmj/1138044041

Digital Object Identifier
doi:10.2996/kmj/1138044041

Mathematical Reviews number (MathSciNet)
MR1700591

Zentralblatt MATH identifier
0957.14015

Subjects
Primary: 14F20: Étale and other Grothendieck topologies and (co)homologies
Secondary: 14F25: Classical real and complex (co)homology 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10]

Citation

Kato, Kazuya; Nakayama, Chikara. Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over ${\bf C}$. Kodai Math. J. 22 (1999), no. 2, 161--186. doi:10.2996/kmj/1138044041. http://projecteuclid.org/euclid.kmj/1138044041.


Export citation

References

  • [AGrV] M. ARTIN, A. GROTHENDIECK AND J. -L. VERDIER, Theone des topos et cohomologie etale des schemas (SGA4), Lecture Notes in Math., 269, 270, 305, Springer, 1972-73.
  • [Dl] P. DELIGNE, Equations differentielles a points singuliers reguliers, Lecture Notes i Math., 163, Springer, 1970.
  • [D2] P. DELIGNE, Theone de Hodge, II, Inst. Hautes Etudes Sci. Publ. Math., 40 (1971), pp.5-58
  • [Fuj] T. FUJISAWA, An Integral structure on a log de Rham complex, in preparation
  • [Ful] W. FULTON, Introduction to Tone Varieties, Ann. of Math. Stud., 131, Pnceto University Press, Princeton, 1993.
  • [FK] K. FUJIWARA AND K. KATO, Logarithmic etale topology theory, preprint
  • [Go] R. GODEMENT, Topologie Algebques et Theone des Faisceaux, Hermann, Pans, 1958
  • [Grl] A. GROTHENDIECK, Seminaire Henri Cartan 1960/61, Ecole Normale Supeneure, Pans, Expose IX.
  • [Gr2] A. GROTHENDIECK, On the de Rham cohomology of algebraic varieties, Inst. Haute Etudes Sci. Publ. Math, 29 (1966), pp. 95-103.
  • [Gr3] A. GROTHENDIECK, Revetements etale et groupe fondamental (SGA1), Lecture Notes i Math, 224, Springer, 1971.
  • [I] L. ILLUSIE, Logarithmic spaces (according to K. Kato), in Barsotti Symposium i Algebraic Geometry (Ed. V Cstante, W Messing), Perspect. Math, 15, Academic Press, 1994, pp. 183-203.
  • [K] K. KATO, Logarithmic structures of Fontaine-IIIusie, Algebraic Analysis, Geometry, and Number Theory (Igusa, J. -I, ed.), Johns Hopkins University Press, Baltimore, 1989, pp.191-224
  • [KKMS] G. KEMPF, F KNUDSEN, D. MUMFORD AND B. SAINT-DONAT, Toroidal embeddings, I, Lecture Notes m Math, 339, Springer, 1973
  • [KN] Y. KAWAMATA AND Y. NAMIKAWA, Logarithmic deformations of normal crossing varietie and smoothing of degenerate Calabi-Yau varieties, Invent. Math, 118(1994), pp. 395-409.
  • [M] H. MAJIMA, Asymptotic analysis for integrable connections with irregular singula points, Lecture Notes in Math, 1075, Springer, 1984.
  • [Nl] C. NAKAYAMA, Logarithmic etale cohomology, Math. Ann, 308(1997), pp. 365-404
  • [N2] C. NAKAYAMA, Nearby cycles for log smooth families, Compositio Math, 112 (1998), pp.45-75
  • [O] A. OGUS, Logarithmic de Rham cohomology, preprint
  • [P] U. PERSSON, On Degeneration of Surfaces, Mem. Amer. Math. Soc, 189, 1977
  • [S] J. H. M. STEENBRINK, Logarithmic embeddings of varieties with normal crossings an mixed Hodge structures, Math. Ann, 301 (1995), pp. 105-118.
  • [V] J. -L. VERDIER, Dualite dans la cohomologie desespaces localement compacts, Seminair Bourbaki 1965/66 300.