Log Betti Cohomology, Log Étale Cohomology, and Log De Rham Cohomology of Log Schemes Over C

Kodai Mathematical Journal

Volumn 22, Issue 2, 1999, Pages 161-186

  Kato, Kazuya ^a   Nakayama, Chikara ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85002450768     PISSN: 03865991     EISSN: None     Source Type: Journal    
DOI: 10.2996/kmj/1138044041     Document Type: Article

References (21)

1. 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.
2. P. Deligne, Equations differentielles a points singuliers reguliers, Lecture Notes in Math., 163, Springer, 1970.
3. P. Deligne, Theone de Hodge, II, Inst. Hautes Etudes Sci. Publ. Math., 40 (1971), pp. 5–58.
4. T. Fujisawa, An Integral structure on a log de Rham complex, in preparation.
5. W. Fulton, Introduction to Toric Varieties, Ann. of Math. Stud., 131, Princeton University Press, Princeton, 1993.
6. K. Fujiwara and K. Kato, Logarithmic etale topology theory, preprint.
7. R. Godement, Topologie Algebnques et Theone des Faisceaux, Hermann, Pans, 1958.
8. A. Grothendieck, Seminaire Henri Cartan 1960/61, Ecole Normale Supeneure, Paris, Expose IX.
9. A. Grothendieck, On the de Rham cohomology of algebraic varieties, Inst. Hautes Etudes Sci. Publ. Math., 29 (1966), pp. 95–103.
10. A. Grothendieck, Revetements etale et groupe fondamental (SGA1), Lecture Notes in Math., 224, Springer, 1971.
11. L. Illusie, Logarithmic spaces (according to K. Kato), in Barsotti Symposium in Algebraic Geometry (Ed. V. Cnstante, W. Messing), Perspect. Math., 15, Academic Press, 1994, pp. 183–203.
12. K. Kato, Logarithmic structures of Fontaine-Illusie, Algebraic Analysis, Geometry, and Number Theory (Igusa, J.-I., ed.), Johns Hopkins University Press, Baltimore, 1989, pp. 191–224.
13. G. Kempf, F. Knudsen, D. Mumford and B. Saint-Donat, Toroidal embeddings, I, Lecture Notes in Math., 339, Springer, 1973.
14. Y. Kawamata and Y. Namikawa, Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties, Invent. Math., 118 (1994), pp. 395–409.
15. H. Majima, Asymptotic analysis for integrable connections with irregular singular points, Lecture Notes in Math., 1075, Springer, 1984.
16. C. Nakayama, Logarithmic etale cohomology, Math. Ann., 308 (1997), pp. 365–404.
17. C. Nakayama, Nearby cycles for log smooth families, Compositio Math., 112 (1998), pp. 45–75.
18. A. Ogus, Logarithmic de Rham cohomology, preprint.
19. U. Persson, On Degeneration of Surfaces, Mem. Amer. Math. Soc., 189, 1977.
20. J. H. M. Steenbrink, Logarithmic embeddings of varieties with normal crossings and mixed Hodge structures, Math. Ann., 301 (1995), pp. 105–118.
21. J.-L. Verdier, Dualite dans la cohomologie des espaces localement compacts, Seminaire Bourbaki 1965-66 n° 300.