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On Saltman’s p-Adic Curves Papers

  • Eric Brussel
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 18)

Summary

We present a synthesis of Saltman’s work (Adv. Math. 43(3):250–283, 1982; J. Alg. 314(2):817–843, 2007) on the division algebras of prime-to-p degree over the function field K of a p-adic curve. Suppose Δ is a K-division algebra. We prove that (a) Δ’s degree divides the square of its period; (b) if Δ has prime degree (different from p), then it is cyclic; (c) Δ has prime index different from p if and only if Δ’s period is prime, and its ramification locus on a certain model for K has no “hot points”.

Keywords

Irreducible Component Nodal Point Division Algebra Curve Point Normal Crossing 
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Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Department of Mathematics & Computer ScienceEmory UniversityAtlantaUSA

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