J Austral Math Soc Ser A 51 pp400--422, 1991.

Large Transcendence Degree

Robert Tubbs

Abstract

In this paper we study the transcendence degree of fields generated over Q by the numbers associated with values of one-parameter subgroups of commutative algebraic groups. We show that in many instances these fields have a large transcendence degree when measured in terms of the available data. Our method deals with points which are "well distributed" (in a sense which is made precise) among certain algebraic subgroups of the algebraic group under consideration. We verify that these results apply in many classical situations.

1991 AMS Subject Classification: 11J99

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Authors

Robert Tubbs

University of Colorado, Boulder, Colorado 80309-0426, U.S.A.