English

Musings on $\Q(1/4)$: Arithmetic spin structures on elliptic curves

Algebraic Geometry 2013-06-14 v1

Abstract

We introduce and study arithmetic spin structures on elliptic curves. We show that there is a unique isogeny class of elliptic curves over \Fp2\F_{p^2} which carries a unique arithmetic spin structure and provides a geometric object of weight 1/2 in the sense of Deligne and Grothendieck. This object is thus a candidate for \Q(1/4)\Q(1/4).

Keywords

Cite

@article{arxiv.1005.3008,
  title  = {Musings on $\Q(1/4)$: Arithmetic spin structures on elliptic curves},
  author = {Kirti Joshi},
  journal= {arXiv preprint arXiv:1005.3008},
  year   = {2013}
}
R2 v1 2026-06-21T15:23:59.967Z