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International Mathematics Research Notices (2000) 2000:353-370, doi:10.1155/S1073792800000209
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Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

Cartier points on curves

Matthew H. Baker

While studying ramified torsion points on curves, Robert Coleman was naturally led to the study of points P on a curve in characteristic P having the property that the Cartier operator preserves the hyperplane of regular differentials vanishing at P. We call such points Cartier points and investigate some of their basic properties. For example, we show that Cartier points, like Weierstrass points, are characterized by a certain gap property.

During our investigation of Cartier points, we strengthen some results of Coleman and Ekedahl. In particular, we obtain a new proof of Ekedahl's theorem bounding the genus of a superspecial curve in characteristic P. We also obtain bounds for the number of Cartier points a curve can have, which in light of Coleman's work has applications to studying torsion points on curves. Finally, we determine the complete set of Cartier points on some specific curves.


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