
TL;DR
This paper explores the combinatorial and scheme-theoretic foundations of finite geometry over the field with one element, including zeta functions of Deitmar schemes, highlighting recent developments.
Contribution
It introduces ideas based on $\
Findings
Connections between combinatorial theory and $\
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contribution
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 , the field with one element. In a second part, I describe, in a nutshell, the fundamental scheme theory over 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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Mathematical Identities · Advanced Algebra and Geometry
