A Chip-Firing and a Riemann-Roch Theorem on an Ultrametric Space

Atsushi Atsuji, Hiroshi Kaneko

研究成果: Conference contribution

抄録

A Riemann-Roch theorem on an edge-weighted infinite graph with local finiteness was established by the present authors in [1], where the spectral gap of Laplacian associated determined by the edge-weight was investigated as the corner stone of the proof. On the other hand, as for non-archimedean metric space, the Laplacians in the construction of Hunt processes such as in [3, 5] based on the Dirichlet space theory can be highlighted. However, in those studies, a positive edge-weight was given substantially between each pair of balls with an identical diameter with respect to the ultrametric and the spectral gap is infeasible. In the present article, we rethink the notion of chip-firing and show an upper bound of function given by accumulation of chip-firing to materialize a counterpart of the dimension of linear system in ultrametric space. In the final section of this article, we establish a Riemann-Roch theorem on an ultrametric space.

本文言語English
ホスト出版物のタイトルDirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022
編集者Zhen-Qing Chen, Masayoshi Takeda, Toshihiro Uemura
出版社Springer
ページ23-43
ページ数21
ISBN(印刷版)9789811946714
DOI
出版ステータスPublished - 2022
イベントInternational Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 - Osaka, Japan
継続期間: 2022 8月 222022 8月 26

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
394
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

Conference

ConferenceInternational Conference on Dirichlet Forms and Related Topics, IWDFRT 2022
国/地域Japan
CityOsaka
Period22/8/2222/8/26

ASJC Scopus subject areas

  • 数学 (全般)

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