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- Title
The group of units on an affine variety.
- Authors
Ford, Timothy J.
- Abstract
The object of study is the group of units 풪*(X) in the coordinate ring of a normal affine variety X over an algebraically closed field k. Methods of Galois cohomology are applied to those varieties that can be presented as a finite cyclic cover of a rational variety. On a cyclic cover X → 픸m of affine m-space over k such that the ramification divisor is irreducible and the degree is prime, it is shown that 풪*(X) is equal to k*, the non-zero scalars. The same conclusion holds, if X is a sufficiently general affine hyperelliptic curve. If X has a projective completion such that the divisor at infinity has r components, then sufficient conditions are given for 풪*(X)/k* to be isomorphic to ℤ(r-1).
- Subjects
GROUP theory; VARIETIES (Universal algebra); COORDINATES; RING theory; GALOIS cohomology; DIVISOR theory
- Publication
Journal of Algebra & Its Applications, 2014, Vol 13, Issue 8, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498814500650