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Proceedings of the American Mathematical Society

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Lifting divisors with imposed ramifications on a generic chain of loops


Author: Xiang He
Journal: Proc. Amer. Math. Soc. 146 (2018), 4591-4604
MSC (2010): Primary 14H10, 14H51, 14M25, 14N10, 14T05; Secondary 12K10, 52B20
DOI: https://doi.org/10.1090/proc/14162
Published electronically: July 23, 2018
MathSciNet review: 3856130
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Abstract: Let $ C$ be a curve over an algebraically closed non-archimedean field with non-trivial valuation. Suppose $ C$ has totally split reduction and the skeleton $ \Gamma $ is a chain of loops with generic edge lengths. Let $ P$ be the rightmost vertex of $ \Gamma $ and let $ \mathcal {P}\in C$ be a point that specializes to $ P$. We prove that any divisor class on $ \Gamma $ with imposed ramification at $ P$ that is rational over the value group of the base field lifts to a divisor class on $ C$ that satisfies the same ramification at $ \mathcal {P}$, which extends the result in [Canad. Math. Bull. 58 (2015), 250-262].


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Additional Information

Xiang He
Affiliation: Department of Mathematics, University of California, Davis, California 95616-8633
Email: unihe@ucdavis.edu

DOI: https://doi.org/10.1090/proc/14162
Received by editor(s): October 29, 2017
Received by editor(s) in revised form: January 12, 2018
Published electronically: July 23, 2018
Communicated by: Lev Borisov
Article copyright: © Copyright 2018 American Mathematical Society