Cyclicity and indecomposability in the Brauer group of a p-adic curve

2018/02/07 by Eduardo Tengan, Tengan, Eduardo
Mathematics · #16 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1802.02322

openalex publication_date 2018/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a p-adic curve X, we study conditions under which all classes in the n-torsion of Br(X) are ℤ/n-cyclic. We show that in general not all classes are ℤ/n-cyclic classes. On the other hand, if X has good reduction and n is prime to p, of if X is an elliptic curve over ℚ_p with split multiplicative reduction and n is a power of p, then we prove that all order n elements of Br(X) are ℤ/n-cyclic. Finally, if X has good reduction and its function field K(X) contains all p²-th roots of 1, we show the existence of indecomposable division algebras over K(X) with period p² and index p³.

Related

• Cyclic Length in the Tame Brauer Group of the Function Field of a p-Adic Curve
• Cyclic Algebras over p-adic curves
• Division Algebra Cyclicity in Prime Degree over a p-Adic Curve
• Tame division algebras of prime period over function fields of p-adic curves
• Curves C that are Cyclic Twists of Y² = X³+c and the Relative Brauer Groups Br(k(C)/k