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Logarithmic Abelian Varieties

Published online by Cambridge University Press:  11 January 2016

Takeshi Kajiwara
Affiliation:
Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Yokohama, 240-8501, Japan, [email protected]
Kazuya Kato
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan, [email protected]
Chikara Nakayama
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo 152-8551, Japan, [email protected]
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Abstract

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We develop the algebraic theory of log abelian varieties. This is Part II of our series of papers on log abelian varieties, and is an algebraic counterpart of the previous Part I ([6]), where we developed the analytic theory of log abelian varieties.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

References

[1] Deligne, P. and Rapoport, M., Les schemas de modules de courbes elliptiques, Modular functions of one variable, II, Antwerp 1972 Preceedings (Deligne, P. and Kuyk, W., eds.), Lecture Notes in Math. 349, Berlin, Springer-Verlag, 1973, pp. 143316.Google Scholar
[2] Faltings, G. and Chai, C., Degeneration of abelian varieties, Ergebnisse der Mathe-matik und ihrer Grenzgebiete 3.Folge·Band 22, Springer-Verlag, Berlin, 1990.Google Scholar
[3] Fujiwara, K., Arithmetic compactifications of Shimura varieties (I), preprint (1990).Google Scholar
[4] Grothendieck, A. and Dieudonne, J. A., Etude cohomologique des faisceaux cohèrents (EGA III), Publ. Math., Inst. Hautes Etud. Sci. 11 (1961), 17 (1963).Google Scholar
[5] Illusie, L., An overview of the work of Fujiwara, K., Kato, K., and Nakayama, C. on logarithmic ètale cohomology, Cohomologies p-adiques et applications Arithmètiques (II) (Berthelot, P., Fontaine, J. M., Illusie, L., Kato, K. and Rapoport, M., ed.), Astèrisque 279, 2002, pp. 271322.Google Scholar
[6] Kajiwara, T., Kato, K., and Nakayama, C., Logarithmic abelian varieties, Part I: Complex analytic theory, to appear in J. Math. Sci. Univ. Tokyo.Google Scholar
[7] Kato, K., Logarithmic structures of Fontaine-Illusie, Algebraic analysis, geometry, and number theory (Igusa, J.-I., ed.), Johns Hopkins University Press, Baltimore, 1989, pp. 191224.Google Scholar
[8] Kato, K., Toric singularities, Amer. J. Math., 116 (1994), 10731099.Google Scholar
[9] Kato, K. and Nakayama, C., Log Betti cohomology, log ètale cohomology, and log de Rham cohomology of log schemes over C, Kodai Math. J., 22 (1999), 161186.CrossRefGoogle Scholar
[10] Nakayama, C., Logarithmic ètale cohomology, Math. Ann., 308 (1997), 365404.Google Scholar
[11] Olsson, M. C., Log algebraic stacks and moduli of log schemes, preprint.Google Scholar
[12] Pahnke, V., Uniformisierung log-abelscher Varietäten, Doctor thesis, Universität Ulm (2005).Google Scholar
[13] Roquette, P., Analytic theory of elliptic functions over local fields, Hamb. Math. Einzelschriften. Neue Folge·Heft 1, Vandenhoeck & Ruprecht in Göttingen, 1970.Google Scholar
[14] Silverman, J. H., The arithmetic of elliptic curves, Graduate texts in mathematics; 106, Springer-Verlag, 1986.CrossRefGoogle Scholar