Vol. 15, No. 1, 2017

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Counting points and acquiring flesh

Koen Thas

Vol. 15 (2017), No. 1, 229–264
Abstract

This set of notes is based on a lecture I gave at “50 years of Finite Geometry: A conference on the occasion of Jef Thas’s 70th birthday,” in November 2014. It consists essentially of three parts: in a first part, I introduce some ideas which are based in the combinatorial theory underlying F1, the field with one element. In a second part, I describe, in a nutshell, the fundamental scheme theory over F1 which was designed by Deitmar. The last part focuses on zeta functions of Deitmar schemes, and also presents more recent work done in this area.

Keywords
Field with one element, Deitmar scheme, loose graph, zeta function, Weyl geometry
Mathematical Subject Classification 2010
Primary: 11G25, 14A15, 14G15
Milestones
Received: 17 August 2015
Accepted: 23 April 2017
Authors
Koen Thas
Department of Mathematics: Algebra and Geometry
Ghent University
Belgium