Abstract
Fix a non-negative integer g and a positive integer I dividing 2g − 2. For any Henselian, discretely valued field K whose residue field is perfect and admits a degree I cyclic extension, we construct a curve C /K of genus g and index I. This is obtained via a systematic analysis of local points on arithmetic surfaces with semistable reduction. Applications are discussed to the corresponding problem over number fields.
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Clark, P.L. On the indices of curves over local fields. manuscripta math. 124, 411–426 (2007). https://doi.org/10.1007/s00229-007-0126-y
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DOI: https://doi.org/10.1007/s00229-007-0126-y