Lifting divisors with imposed ramifications on a generic chain of loops
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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].References
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Additional Information
- Xiang He
- Affiliation: Department of Mathematics, University of California, Davis, California 95616-8633
- Email: unihe@ucdavis.edu
- 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
- © Copyright 2018 American Mathematical Society
- 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
- MathSciNet review: 3856130