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Prehomogeneous vector spaces and field extensions

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Letk be an infinite field of characteristic not equal to 2, 3, 5. In this paper, we construct a natural map from the set of orbits of certain prehomogeneous vector spaces to the set of isomorphism classes of Galois extensions ofk which are splitting fields of equations of certain degrees, and prove that the inverse image of this map corresponds bijectively with conjugacy classes of Galois homomorphisms.

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Authors and Affiliations

  1. Mathematics Department, College of Arts and Sciences, Oklahoma State University, 74078, Stillwater, OK, USA

    David J. Wright & Akihiko Yukie

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  1. David J. Wright
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  2. Akihiko Yukie
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Oblatum 24-I-1992 & 23-IV-1992

Both authors are supported by NSF Grant DMS-8803085, DMS-9101091; The first author was partially supported by NSA grant MDA904-91-H-0041

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Wright, D.J., Yukie, A. Prehomogeneous vector spaces and field extensions. Invent Math 110, 283–314 (1992). https://doi.org/10.1007/BF01231334

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