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Functoriality of Moduli Spaces of Global $\mathbb G$-Shtukas

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arxiv 1902.10602 v1 pith:JYAWYWCY submitted 2019-02-27 math.AG math.NT

Paul Breutmann This is my paper · ORCID
classification math.AGmath.NT
keywords mathbbglobalmodulishtukasspaceschangefunctorialityallow
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abstract

Moduli spaces of global $\mathbb G$-shtukas play a crucial role in the Langlands program for function fields. We analyze their functoriality properties following a change of the curve and a change of the group scheme $\mathbb G$ under various aspects. In particular, we prove two finiteness results which are of interest in the study of stratifications of these moduli spaces and which potentially allow the formulation of an analog of the Andr\'{e}-Oort conjecture for global $\mathbb G$-shtukas.

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  1. Introduction to Shtukas and their moduli

    math.NT 2024-11 unverdicted

    A survey of Shtukas and their moduli stacks, written as lecture notes, covering definitions, geometry, cohomological structures, and applications.

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