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Reduction in the Rationality Problem for Multiplicative Invariant Fields

✍ Scribed by Nicole Marie Anne Lemire

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
228 KB
Volume
238
Category
Article
ISSN
0021-8693

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✦ Synopsis

For a faithful ZG lattice A and a field K on which the group G acts by field automorphisms, let R be the normal subgroup generated by the elements of G which act trivially on K and act as reflections on A. We prove that the rationality

G such that GrR ( ⍀ . We then use this reduction result to prove that K A is G rational over K where G is the automorphism group of a crystallographic root system ⌿, G acts trivially on K and A is any lattice on the space Q⌿.

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