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August 9, 2026Journal of the Institute of Mathematics of JussieuOpen Access

On Spectral Sequences for Semiabelian Varieties Over Non-Closed Fields

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Authors

APAlexander PetrovASAlexei N. Skorobogatov

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Overview

New proof clarifies differential behavior in spectral sequences for semiabelian varieties, indicating important algebraic properties.

Key Points

  • This work aims to provide a concise proof of the differential formula in the Hochschild–Serre spectral sequence for semiabelian varieties over non-closed fields.
  • Proved a formula for the first potentially non-zero differential of the Hochschild–Serre spectral sequence
  • Analyzed cases where the Jacobian of a curve shows non-trivial differentials
  • Generalized previous results on differentials for smooth projective curves
  • The differential is shown to be non-zero for the Jacobian of a curve with specific torsor properties
  • When the Albanese torsor is trivial, the spectral sequence degenerates at the second page
  • A new formula is provided for the Brauer group of a torus based on the Hochschild–Serre spectral sequence

Cite This Study

Petrov et al. (2026) studied this question.

synapsesocial.com/papers/6a782cb82e1896536c83f97ahttps://doi.org/10.1017/s1474748026101753
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