Sampling spaces and arithmetic dimension

Catherine O’Neil ()

A chapter in Number Theory, Analysis and Geometry, 2012, pp 499-518 from Springer

Abstract: Abstract This paper introduces the twin concepts of sampling spaces and arithmetic dimension, which together address the question of how to count the number, or measure the size of, families of objects over a number field or global field. It can be seen as an alternative to coarse moduli schemes, with more attention to the arithmetic properties of the ambient base field, and which leads to concrete algorithmic applications and natural height functions. It is compared to the definition of essential dimension.

Keywords: essential dimension; coarse moduli; elliptic curves (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-1260-1_23

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DOI: 10.1007/978-1-4614-1260-1_23

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