Torsors of the Jacobians of the generic Fermat curves

Time：Wed., 15:30-16:30 Oct. 9, 2024

Venue：C654, Shuangqing Complex Building

Organizer：Xiang He, Chenglong Yu, Dingxin Zhang, Jie Zhou

Speaker：Qixiao Ma

Moduli Spaces and Related Topics

Organizers：

Xiang He, Chenglong Yu, Dingxin Zhang, Jie Zhou

Speaker：

Qixiao Ma 马骐骁

ShanghaiTech University

Time：

Wed., 15:30-16:30

Oct. 9, 2024

Venue：

C654, Shuangqing Complex Building

清华大学双清综合楼A座 C654

Title:

Torsors of the Jacobians of the generic Fermat curves

Abstract：

Let C/S be the universal family of degree m (m>3) Fermat curve. Then A=Pic^0_{C/S} is an abelian scheme over S. We show that: (1) All torsors of A/S are of the form Pic^d_{C/S}. (2) Passing to the function field, there are uncountably many non-isomorphic torsors of A_k(S). Finally we discuss some partial results on extending the result to M_g.

DATEOctober 8, 2024

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