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A Gelfand–Beurling Type Formula for Heights on Endomorphism Rings

✍ Scribed by Valerio Talamanca

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 158 KB
Volume: 83
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2506

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✦ Synopsis

Let V be a finite-dimensional vector space over a number field. In this paper we prove a limit formula for heights on the endomorphism ring of V, which can be considered as the analogue for both the Gelfand Beurling formula for the spectral radius on a Banach algebra and Tate's averaging procedure for constructing canonical heights on abelian varieties. We also prove a version of Northcott's finiteness theorem.