An asymptotic estimate for heights of algebraic subspaces

Thunder, Jeffrey Lin

doi:10.1090/S0002-9947-1992-1072102-0

An asymptotic estimate for heights of algebraic subspaces
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by Jeffrey Lin Thunder PDF

Trans. Amer. Math. Soc. 331 (1992), 395-424 Request permission

Abstract:

We count the number of subspaces of affine space with a given dimension defined over an algebraic number field with height less than or equal to $B$. We give an explicit asymptotic estimate for the number of such subspaces as $B$ goes to infinity, where the constants involved depend on the classical invariants of the number field (degree, discriminant, class number, etc.). The problem is reformulated as an estimate for the number of lattice points in a certain bounded domain.

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