Arithmetic in the fundamental group of a p-adic curve: On the p-adic section conjecture for curves

Details Arithmetic in the fundamental group of a p-adic curve: On the p-adic section conjecture for curves Arithmetic in the fundamental group of a p-adic curve: On the p-adic section conjecture for curves

2011-11-05

arxiv.org/abs/1111.1354v1

Mathematics

Algebraic Geometry

32 pages, 4 figures, with an appendix on the zoo of valuations for 2-dimensional semi local fields

Scientific paper

We establish a valuative version of Grothendieck's section conjecture for
curves over p-adic local fields. The image of every section is contained in the
decomposition subgroup of a valuation which prolongs the p-adic valuation to
the function field of the curve.

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