Relative Brauer groups of genus 1 curves

Mirela Ciperiani, Daniel Krashen

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


In this paper we develop techniques for computing the relative Brauer group of curves, focusing particularly on the case where the genus is 1. We use these techniques to show that the relative Brauer group may be infinite (for certain ground fields) as well as to determine this group explicitly for certain curves defined over the rational numbers. To connect to previous descriptions of relative Brauer groups in the literature, we describe a family of genus 1 curves, which we call "cyclic type" for which the relative Brauer group can be shown to have a particularly nice description. In order to do this, we discuss a number of formulations of the pairing between the points on an elliptic curve and its Weil-Chatêlet group into the Brauer group of the ground field, and draw connections to the period-index problem for genus 1 curves.

Original languageEnglish (US)
Pages (from-to)921-949
Number of pages29
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Nov 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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