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Fields with measure and automorphism
Author(s) -
Tomašić Ivan
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp013
Subject(s) - mathematics , genus , automorphism , automorphism group , measure (data warehouse) , affine transformation , pure mathematics , finite field , field (mathematics) , combinatorics , zoology , database , biology , computer science
We consider a difference field ( K , σ) such that finite‐dimensional definable sets over K can be compared in size, or measured. Let k be the fixed field of the automorphism σ. 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.