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5 results

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

  • Takeshi Kajiwara, Kazuya Kato, Chikara Nakayama
  • Journal: Nagoya Mathematical Journal / Volume 210 / June 2013
  • Published online by Cambridge University Press: 11 January 2016, pp. 59-81
  • Print publication: June 2013
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  • We illustrate the theory of log abelian varieties and their moduli in the case of log elliptic curves.

  • Analytic Log Picard Varieties

  • Takeshi Kajiwara, Kazuya Kato, Chikara Nakayama
  • Journal: Nagoya Mathematical Journal / Volume 191 / 2008
  • Published online by Cambridge University Press: 11 January 2016, pp. 149-180
  • Print publication: 2008
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  • We introduce a log Picard variety over the complex number field by the method of log geometry in the sense of Fontaine-Illusie, and study its basic properties, especially, its relationship with the group of log version of m-torsors.

  • Logarithmic Abelian Varieties

  • Takeshi Kajiwara, Kazuya Kato, Chikara Nakayama
  • Journal: Nagoya Mathematical Journal / Volume 189 / 2008
  • Published online by Cambridge University Press: 11 January 2016, pp. 63-138
  • Print publication: 2008
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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.

  • Nearby cycles for log smooth families

  • CHIKARA NAKAYAMA
  • Journal: Compositio Mathematica / Volume 112 / Issue 1 / May 1998
  • Published online by Cambridge University Press: 04 December 2007, pp. 45-75
  • Print publication: May 1998
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  • We calculate l-adic nearby cycles in the étale cohomology for families with log smooth reduction using log étale cohomology. In particular, nearby cycles for log smooth families coincide with tame nearby cycles, as L. Illusie expected, and nearby cycles for semistable families depend only on the first infinitesimal neighborhood of the special fiber.