Torsion points on Jacobian varieties via Anderson's p-adic soliton theory

Shinichi Kobayashi, Takao Yamazaki

Research output: Contribution to journalArticle

Abstract

Anderson introduced a p-adic version of soliton theory. He then applied it to the Jacobian variety of a cyclic quotient of a Fermat curve and showed that torsion points of certain prime order lay outside of the theta divisor. In this paper, we evolve his theory further. As an application, we get a stronger result on the intersection of the theta divisor and torsion points on the Jacobian variety for more general curves. New examples are discussed as well. A key new ingredient is a map connecting the p-adic loop group and the formal group.

Original languageEnglish
Pages (from-to)323-352
Number of pages30
JournalAsian Journal of Mathematics
Volume20
Issue number2
DOIs
Publication statusPublished - Jan 1 2016
Externally publishedYes

Fingerprint

Theta Divisor
Jacobian Varieties
Torsion Points
Solitons
P-adic
Torsional stress
Fermat Curve
Formal Group
P-adic Groups
Loop Groups
Quotient
Intersection
Curve

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Torsion points on Jacobian varieties via Anderson's p-adic soliton theory. / Kobayashi, Shinichi; Yamazaki, Takao.

In: Asian Journal of Mathematics, Vol. 20, No. 2, 01.01.2016, p. 323-352.

Research output: Contribution to journalArticle

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