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

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

2010-05-17

arxiv.org/abs/1005.3008v1

Mathematics

Algebraic Geometry

Scientific paper

We introduce and study arithmetic spin structures on elliptic curves. We show
that there is a unique isogeny class of elliptic curves over $\F_{p^2}$ 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 $\Q(1/4)$.

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