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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



More étale covers of affine spaces in positive characteristic

Author: Kiran S. Kedlaya
Journal: J. Algebraic Geom. 14 (2005), 187-192
Published electronically: July 13, 2004
MathSciNet review: 2092132
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Abstract | References | Additional Information

Abstract: We prove that every geometrically reduced projective variety of pure dimension $n$ over a field of positive characteristic admits a morphism to projective $n$-space, étale away from the hyperplane $H$ at infinity, which maps a chosen divisor into $H$ and some chosen smooth points not on the divisor to points not in $H$. This improves an earlier result of the author, which was restricted to infinite perfect fields. We also prove a related result that controls the behavior of divisors through the chosen point.

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Additional Information

Kiran S. Kedlaya
Affiliation: Department of Mathematics, Room 2-165, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
MR Author ID: 349028
ORCID: 0000-0001-8700-8758

Received by editor(s): July 1, 2003
Received by editor(s) in revised form: December 12, 2003
Published electronically: July 13, 2004
Additional Notes: Supported by a National Science Foundation postdoctoral fellowship.