Moduli of finite flat torsors over nodal curves

Sara Mehidi; Thibault  Poiret

doi:10.1112/jlms.70220

Moduli of finite flat torsors over nodal curves

Sara Mehidi, Thibault Poiret^*

^*Corresponding author for this work

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that log flat torsors over a family 𝑋∕𝑆 of nodal curves under a finite flat commutative group scheme 𝐺∕𝑆 are classified by maps from the Cartier dual of 𝐺 to the log Jacobian of 𝑋. We deduce that fppf torsors on the smooth fiberss of 𝑋∕𝑆 can be extended to global log flat torsors under some regularity hypotheses.

Original language	English
Article number	e70220
Number of pages	33
Journal	Journal of the London Mathematical Society
Volume	112
Issue number	1
Early online date	25 Jun 2025
DOIs	https://doi.org/10.1112/jlms.70220
Publication status	Published - 1 Jul 2025

Access to Document

10.1112/jlms.70220Licence: CC BY

Mehidi_2025_JLMS_Moduli-finite-flat-torsors-nodal-curves_CC
© 2025 The Author(s). This is an open access article under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Final published version, 679 KBLicence: CC BY

Tropical Geometry and the moduli space o: Tropical Geometry and the moduli space of Prym varieties
Len, Y. (PI)
EPSRC
1/05/23 → 31/10/25
Project: Standard

Cite this

@article{1cda8b11b1144d67a3b2f0b54acb60d1,

title = "Moduli of finite flat torsors over nodal curves",

abstract = "We show that log flat torsors over a family 𝑋∕𝑆 of nodal curves under a finite flat commutative group scheme 𝐺∕𝑆 are classified by maps from the Cartier dual of 𝐺 to the log Jacobian of 𝑋. We deduce that fppf torsors on the smooth fiberss of 𝑋∕𝑆 can be extended to global log flat torsors under some regularity hypotheses.",

author = "Sara Mehidi and Thibault Poiret",

note = "Funding: The authors thank the Institut de Math{\'e}matiques de Bordeaux for funding a research visit of T. Poiret to Bordeaux. S. Mehidi was funded partially by the Dutch Research Council (NWO) grant VI.Vidi.213.019, which also funded a research visit of T. Poiret to Utrecht. T. Poiret was funded partially by EPSRC New Investigator Grant EP/V051830/1 and by EPSRC New Investigator award EP/X002004/1.",

year = "2025",

month = jul,

day = "1",

doi = "10.1112/jlms.70220",

language = "English",

volume = "112",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "Oxford University Press",

number = "1",

}

TY - JOUR

T1 - Moduli of finite flat torsors over nodal curves

AU - Mehidi, Sara

AU - Poiret, Thibault

N1 - Funding: The authors thank the Institut de Mathématiques de Bordeaux for funding a research visit of T. Poiret to Bordeaux. S. Mehidi was funded partially by the Dutch Research Council (NWO) grant VI.Vidi.213.019, which also funded a research visit of T. Poiret to Utrecht. T. Poiret was funded partially by EPSRC New Investigator Grant EP/V051830/1 and by EPSRC New Investigator award EP/X002004/1.

PY - 2025/7/1

Y1 - 2025/7/1

N2 - We show that log flat torsors over a family 𝑋∕𝑆 of nodal curves under a finite flat commutative group scheme 𝐺∕𝑆 are classified by maps from the Cartier dual of 𝐺 to the log Jacobian of 𝑋. We deduce that fppf torsors on the smooth fiberss of 𝑋∕𝑆 can be extended to global log flat torsors under some regularity hypotheses.

AB - We show that log flat torsors over a family 𝑋∕𝑆 of nodal curves under a finite flat commutative group scheme 𝐺∕𝑆 are classified by maps from the Cartier dual of 𝐺 to the log Jacobian of 𝑋. We deduce that fppf torsors on the smooth fiberss of 𝑋∕𝑆 can be extended to global log flat torsors under some regularity hypotheses.

U2 - 10.1112/jlms.70220

DO - 10.1112/jlms.70220

M3 - Article

SN - 0024-6107

VL - 112

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

M1 - e70220

ER -

Moduli of finite flat torsors over nodal curves

Abstract

Access to Document

Fingerprint

Projects

Tropical Geometry and the moduli space o: Tropical Geometry and the moduli space of Prym varieties

Cite this