On $\mathsf{G}$-isoshtukas over function fields

Paul Hamacher; Wansu Kim

On $\mathsf{G}$-isoshtukas over function fields

Algebraic Geometry 2021-06-17 v3 Number Theory

Authors: Paul Hamacher , Wansu Kim

Abstract

In this paper we classify isogeny classes of global $\mathsf{G}$ -shtukas over a smooth projective curve $C/\mathbb{F}_q$ (or equivalently $\sigma$ -conjugacy classes in $\mathsf{G}(\mathsf{F} \otimes_{\mathbb{F}_q} \overline{\mathbb{F}_q})$ where $\mathsf{F}$ is the field of rational functions of $C$ ) by two invariants $\bar\kappa,\bar\nu$ extending previous works of Kottwitz. This result can be applied to study points of moduli spaces of $\mathsf{G}$ -shtukas and thus is helpful to calculate their cohomology.

Cite

@article{arxiv.2003.07389,
  title  = {On $\mathsf{G}$-isoshtukas over function fields},
  author = {Paul Hamacher and Wansu Kim},
  journal= {arXiv preprint arXiv:2003.07389},
  year   = {2021}
}

Comments

26 pages, v3: Added a short exposition of related works in the introduction; elaborated on the localisation map of $\sigma$-conjugacy classes and fixed a minor mistake in the formula of Newton point of the localisation of a $\sigma$-conjugacy class

On $\mathsf{G}$-isoshtukas over function fields

Abstract

Cite

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