THE FUNDAMENTAL GROUP OF AN EXTENSION IN A TANNAKIAN CATEGORY AND THE UNIPOTENT RADICAL OF THE MUMFORD-TATE GROUP OF AN OPEN CURVE

被引：1

作者：

Eskandari, Payman ^{[1
]}

Murty, V. Kumar ^{[2
]}

机构：

[1] Univ Winnipeg, Dept Math & Stat, Winnipeg, MB, Canada

[2] Univ Toronto, Dept Math, Toronto, ON, Canada

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2023年 / 325卷 / 02期

关键词：

Tannakian categories; Mumford-Tate groups; mixed Hodge structures; GALOIS GROUP;

D O I：

10.2140/pjm.2023.325.255

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the first part, we give a self-contained account of Tannakian fundamental groups of extensions, generalizing a result of Hardouin (2008; 2011). In the second part, we use Hardouin's characterization of Tannakian groups of extensions to give a characterization of the unipotent radical of the Mumford- Tate group of an open complex curve. Consequently, we prove a formula that relates the dimension of the unipotent radical of the Mumford-Tate group of an open complex curve X \S with X smooth and projective and S a finite set of points to the rank of the subgroup of the Jacobian of X supported on S.

引用

页码：255 / 279

页数：28

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