The group of units on an affine variety
2014 ◽
Vol 13
(08)
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pp. 1450065
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Keyword(s):
The object of study is the group of units 𝒪*(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 → 𝔸m of affine m-space over k such that the ramification divisor is irreducible and the degree is prime, it is shown that 𝒪*(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 𝒪*(X)/k* to be isomorphic to ℤ(r-1).
2009 ◽
Vol 05
(05)
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pp. 897-910
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1996 ◽
Vol 48
(5)
◽
pp. 1091-1120
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1986 ◽
Vol 29
(2)
◽
pp. 140-145
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Keyword(s):
1958 ◽
Vol 65
(1)
◽
pp. 63-71
1974 ◽
Vol 76
(2)
◽
pp. 465-471
Keyword(s):