More étale covers of affine spaces in positive characteristic

Author(s): Kiran S. Kedlaya
Journal: J. Algebraic Geom. 14 (2005), 187-192.
Posted: July 13, 2004
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Abstract: We prove that every geometrically reduced projective variety of pure dimension over a field of positive characteristic admits a morphism to projective -space, étale away from the hyperplane at infinity, which maps a chosen divisor into and some chosen smooth points not on the divisor to points not in . 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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Kiran S. Kedlaya
Affiliation: Department of Mathematics, Room 2-165, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Email: kedlaya@mit.edu

PII: S 1056-3911(04)00381-9
Received by editor(s): July 1, 2003
Received by editor(s) in revised form: December 12, 2003
Posted: July 13, 2004
Additional Notes: Supported by a National Science Foundation postdoctoral fellowship.