Asian Journal of Mathematics

Volume 24 (2020)

Number 1

Category of mixed plectic Hodge structures

Pages: 31 – 76

DOI: https://dx.doi.org/10.4310/AJM.2020.v24.n1.a2

Authors

Kenichi Bannai (Keio Institute of Pure and Applied Sciences (KiPAS) and Department of Mathematics, Keio University, Yokohama, Japan; and Mathematical Science Team, RIKEN Center for Advanced Intelligence Project, Chuo-ku, Tokyo, Japan)

Kei Hagihara (Department of Mathematics, Keio University, Yokohama, Japan; and Mathematical Science Team, RIKEN Center for Advanced Intelligence Project, Chuo-ku, Tokyo, Japan)

Shinichi Kobayashi (Faculty of Mathematics, Kyushu University, Fukuoka, Japan)

Kazuki Yamada (Department of Mathematics, Keio University, Yokohama, Japan)

Shuji Yamamoto (Keio Institute of Pure and Applied Sciences (KiPAS) and Department of Mathematics,, Keio University, Yokohama, Japan; and Mathematical Science Team, RIKEN Center for Advanced Intelligence Project, Chuo-ku, Tokyo, Japan)

Seidai Yasuda (Department of Mathematics, Osaka University, Osaka, Japan; and Mathematical Science Team, RIKEN Center for Advanced Intelligence Project, Chuo-ku, Tokyo, Japan)

Abstract

The purpose of this article is to investigate the properties of the category of mixed plectic Hodge structures defined by Nekovář and Scholl [NS1]. We give an equivalent description of mixed plectic Hodge structures in terms of the weight and partial Hodge filtrations. We also construct an explicit complex calculating the extension groups in this category.

Keywords

mixed Hodge structures, plectic structures

2010 Mathematics Subject Classification

14C30

Full Text (PDF format)

Research for this paper was conducted as part of the KiPAS program FY2014–2018 of the Faculty of Science and Technology at Keio University, and was supported in part by KAKENHI 26247004, 16J01911, 16K13742, and 18H05233, as well as by the JSPS Core-to-Core program “Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory and Geometry”.

Received 14 June 2017

Accepted 11 April 2019

Published 21 August 2020