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Rationality of Some Projective Linear Actions

✍ Scribed by Hamza Ahmad; Mowaffaq Hajja; Ming-chang Kang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
125 KB
Volume
228
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

THEOREM. If dim V F 3, then both K V and K ‫ސ‬ V are rational K Ε½ . s purely transcendental over K. Similar results hold for a cyclic affine action.

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Let p be a prime number, G a p-group of order ≀ p 4 K a field with char K = p. If the exponent of G is p e and K contains a primitive p e th root of unity, then K V G is rational (=purely transcendental) over K where ρ G β†’ GL V is any linear representation of G over K.

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