Cyclic algebras over p-adic curves
By D. Saltman. 2006
51 citations recorded by the source corpus.
Abstract In this paper we study division algebras over the function fields of curves over Q p . The first and main tool is to view these fields as function fields over nonsingular S which are projective of relative dimension 1 over the p adic ring Z p . A previous paper showed such division algebras had index bounded by n 2 assuming the exponent was n and n was prime to p. In this paper we consider algebras of prime degree (and hence exponent) q ≠ p and show these algebras are cyclic. We also find a geometric criterion for a Brauer class to have index q.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f5f2ca52eb9b3d0c3b27335599da4aac6d44a911
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Period and index in the Brauer group of an arithmetic surface (2007, methodology): “ted to B. Letting W 1 be a regular α-twisted sheaf and W 2a regular β-twisted sheaf, we see that pr∗ 1 W 1 ⊗pr∗ W 2 is a G-twisted sheaf with the requisite properties. 4.3.9. The reader familiar with [33] might notice a resemblance between Proposition 4.3.7 and Saltman’s “meteorology” of points on r”
- The u-invariant of the function fields of p-adic curves (2007, methodology): “Proposition 2.1 ([ S3 ], 1.6) Let Z be a connected, reduced scheme of finite type over a Noetherian ring.”
- Applications of patching to quadratic forms and central simple algebras (2008, unknown): “Therefore [32], Theorem 2.”