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Logarithmic abelian varieties, III: Logarithmic elliptic curves and modular curves

Published online by Cambridge University Press:  11 January 2016

Takeshi Kajiwara ,
Kazuya Kato  and
Chikara Nakayama
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, University of Chicago, Chicago, Illinois, 60637, USA, [email protected]
Chikara Nakayama
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Tokyo 152-8551, Japan, [email protected]
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Abstract

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We illustrate the theory of log abelian varieties and their moduli in the case of log elliptic curves.

Keywords

14K1014J1014D06
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 210 , June 2013 , pp. 59 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

References

[1] Conrad, B., Arithmetic moduli of generalized elliptic curves, J. Inst. Math. Jussieu 6 (2007), 209–278. MR 2311664. DOI 10.1017/S1474748006000089.Google Scholar
[2] Deligne, P. and Rapoport, M., “Les schémas de modules de courbes elliptiques” in Modular Functions of One Variable, II (Antwerp, 1972), Lecture Notes in Math. 349, Springer, Berlin, 1973, 143–316. MR 0337993.Google Scholar
[3] Kajiwara, T., Kato, K., and Nakayama, C., Logarithmic abelian varieties, Nagoya Math. J. 189 (2008), 63–138. MR 2396584.Google Scholar
[4] Kato, K., “Logarithmic structures of Fontaine-Illusie” in Algebraic Analysis, Geometry, and Number Theory (Baltimore, 1988), Johns Hopkins University Press, Baltimore, 1989, 191–224. MR 1463703.Google Scholar
[5] Katz, N. M. and Mazur, B., Arithmetic Moduli of Elliptic Curves, Ann. of Math. Stud. 108, Princeton University Press, Princeton, 1985. MR 0772569.Google Scholar
[6] Nakayama, C., Logarithmic étale cohomology, Math. Ann. 308 (1997), 365–404. MR 1457738. DOI 10.1007/s002080050081.Google Scholar
[7] Olsson, M. C., Log algebraic stacks and moduli of log schemes, Ph.D. dissertation, University of California, Berkeley, Berkeley, California, 2001. MR 2702292.Google Scholar
[8] Stroh, B., Compactification minimale et mauvaise réduction, Ann. Inst. Fourier (Grenoble) 60 (2010), 1035–1055. MR 2680823.Google Scholar