On the ring of unipotent vector bundles on elliptic curves in positive characteristics

Details On the ring of unipotent vector bundles on elliptic curves in positive characteristics On the ring of unipotent vector bundles on elliptic curves in positive characteristics

2009-08-26

arxiv.org/abs/0908.3743v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

Using Fourier-Mukai transformations, we prove some results about the ring of unipotent vector bundles on elliptic curves in positive characteristics. This ring was determined by Atiyah in characteristic zero, who showed that it is a polynomial ring in one variable. It turns out that the situation in characteristic p>0 is completely different and rather bizarre: the ring is nonnoetherian and contains a subring whose spectrum contains infinitely many copies of Spec(Z), which are glued with successively higher and higher infinitesimal identification at the point corresponding to the prime p.

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