Relative Brauer groups of genus 1 curves

DOI10.1007/s11856-012-0057-5zbMath1259.14020arXivmath/0701614OpenAlexW1991615402MaRDI QIDQ1936821

Mirela Ciperiani, Daniel Krashen

Publication date: 7 February 2013

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701614

zbMATH Keywords

Relative Brauer groups

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Finite-dimensional division rings (16K20) Brauer groups of schemes (14F22) Brauer groups (algebraic aspects) (16K50)

Related Items (14)

Cyclic length in the Brauer group of a p-adic elliptic curve ⋮ Relative Brauer groups of torsors of period two ⋮ On some algebras associated to genus one curves ⋮ On the size of the genus of a division algebra ⋮ A positive proportion of cubic curves over Q admit linear determinantal representations ⋮ Unnamed Item ⋮ On cyclic twists of elliptic curves of period two or three and the determination of their relative Brauer groups ⋮ Étale twists in noncommutative algebraic geometry and the twisted Brauer space ⋮ On the generalized Clifford algebra of a monic polynomial ⋮ On an algebra associated to a ternary cubic curve. ⋮ Derived categories of torsors for abelian schemes ⋮ RelBrauer ⋮ Curves $\mathcal{C}$ that are cyclic twists of $Y^{2}=X^{3}+c$ and the relative Brauer groups $Br(k(\mathcal{C})/k)$ ⋮ An algorithm to obtain linear determinantal representations of smooth plane cubics over finite fields

Uses Software

• Macaulay2
• PARI/GP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On an algebra associated to a ternary cubic curve.
• Algebras of odd degree with involution, trace forms and dihedral extensions
• Representing Clifford algebras as crossed-products
• On Azumaya algebras arising from Clifford algebras
• La descente sur les variétés rationnelles. II. (The descent on rational varieties. II)
• When is the Clifford algebra of a binary cubic form split?
• On maps with dense orbits and the definition of chaos
• Index reduction formulas for twisted flag varieties. I
• Duality theorems for curves over p-adic fields
• Curves $\mathcal{C}$ that are cyclic twists of $Y^{2}=X^{3}+c$ and the relative Brauer groups $Br(k(\mathcal{C})/k)$
• Some remark on rational points
• Rational Points of Abelian Varieties Over Function Fields
• Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung.
• Index Reduction for Brauer Classes via Stable Sheaves
• On the Clifford Algebra of a Binary Cubic Form
• Dihedral Algebras are Cyclic
• Relative Brauer Groups of Function Fields of Curves of Genus One
• There are genus one curves of every index over every number field
• Splitting of Algebras by Function Fields of One Variable
• The Period-Index Problem for Elliptic Curves
• Galois Chomology of Cycles and Applications to Elliptic Curves
• Finite-Dimensional Division Algebras over Fields

This page was built for publication: Relative Brauer groups of genus 1 curves