Abstract
This chapter summarizes, with examples but without proof, many of the known properties of algebraic groups relative to fields of definition. As before, K denotes an algebraically closed field. If k is an arbitrary subfield of K, we are interested in the closed subgroups of GL(n, K) which are defined by polynomials with coefficients in k. Some general theory is developed in §34, to be followed by a discussion of special fields (finite, real, p-adic) in §35.
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© 1975 Springer-Verlag New York Inc.
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Humphreys, J.E. (1975). Survey of Rationality Properties. In: Linear Algebraic Groups. Graduate Texts in Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9443-3_12
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DOI: https://doi.org/10.1007/978-1-4684-9443-3_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9445-7
Online ISBN: 978-1-4684-9443-3
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