The Period and Index of a Generic Geometrically Elliptic Normal Curve

Abstract

We construct genus one curves on base extensions of generic Severi--Brauer varieties of a given index and period which are versal objects for families of geometrically elliptic normal curves. We also compute the periods and indices of these curves showing that all possible period/index combinations are possible.

19 pages, Journal of Algebra

References in corpus (2)

• Explicit descent on elliptic curves and splitting Brauer classes
• Genus 1 Curves in Severi--Brauer Surfaces