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On the ring of unipotent vector bundles on elliptic curves in positive characteristics
Author(s) -
Schröer Stefan
Publication year - 2010
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdq028
Subject(s) - unipotent , mathematics , subring , ring (chemistry) , pure mathematics , noetherian ring , finitely generated abelian group , chemistry , organic chemistry
Using Fourier–Mukai transforms, 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 non‐noetherian 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 .