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The Rank of the Cartier Operator and Linear Systems on Curves

โœ Scribed by Riccardo Re

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
97 KB
Volume
236
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

We find bounds for the genus of a curve over a field of characteristic p under the hypothesis that the Cartier operator of this curve has low rank and in the case where it is nilpotent. แฎŠ 2001 Academic Press c w x e.g., 11 . Moreover, we wish to remark that the rank of the Cartier operator on a curve is equal to g y g ะˆ where g is the genus of the curve and g ะˆ is the dimension of the space of locally exact regular differential forms on the curve, i.e., the regular differential forms such that, locally, 80

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