arXiv subjects

Paul Breutmann

Publications and source records attributed to Paul Breutmann.

2 recordsLinked to original sources

arXiv2019

The Carlitz Logarithm as a Period Morphism for Local $G$-Shtukas

Local shtukas are the function field analogs for $p$-divisible groups. Similar to the $p$-adic theory, one defines Rapoport-Zink functors and Rapoport-Zink spaces for these local shtukas. The associated Hodge-Pink structures are described uniquely by a morphism, called the period morphism of the moduli problem. We will prove the ind-representability of the Rapoport-Zink functor in a particular case and compute the corresponding Rapoport-Zink space as well as the corresponding period morphism. In this case, the period morphism is given by the Carlitz logarithm.

math.AG↗

arXiv2019

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

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 André-Oort conjecture for global $\mathbb G$-shtukas.

math.AG↗