More etale covers of affine spaces in positive characteristic

Details More etale covers of affine spaces in positive characteristic More etale covers of affine spaces in positive characteristic

2003-03-31

arxiv.org/abs/math/0303382v3

preprint; published version: J. Alg. Geom. 14 (2005), 187-192.

Mathematics

Algebraic Geometry

6 pages, AMSTeX; v3: some errors fixed; to appear in J. Algebraic Geometry

Scientific paper

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, etale 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 our earlier result in math.AG/0207150, 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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