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arXiv · 1907.06456

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

Paul Breutmann
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Abstract

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.

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Paul Breutmann. 2019-07-15. The Carlitz Logarithm as a Period Morphism for Local $G$-Shtukas. https://arxiv.org/abs/1907.06456

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