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Bulletin of the London Mathematical Society Advance Access originally published online on April 3, 2009
Bulletin of the London Mathematical Society 2009 41(3):429-440; doi:10.1112/blms/bdp013
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© 2009 London Mathematical Society

Fields with measure and automorphism

Ivan Tomasic

School of Mathematics
Queen Mary University of London
London
E1 4NS
United Kingdom

Received 12 October 2006. Revision received 22 October 2008.

We consider a difference field (K, {sigma}) such that finite-dimensional definable sets over K can be compared in size, or measured. Let k be the fixed field of the automorphism {sigma}. We show that curves of genus 1 defined over k are approximately the size of the affine line over k, an ‘approximative version’ of the Riemann hypothesis for curves of genus 1.

2000 Mathematics Subject Classification 03C60, 11G25, 12H10 (primary), 14G10, 14G15 (secondary).


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