Field of characteristic one

introduction

http://at.yorku.ca/cgi-bin/abstract/cbgm-80

The analogies between numbers and functions of one variable were known long ago: integers share common properties with polynomials over rational numbers or over finite fields; p-adic numbers are similar to formal series.

During the last two decades, such analogies have been developed and became background of two fascinating new chapters of algebra/number theory: Alexandru Buium's "Arithmetic Differential Equations" and a collective endeavor "Algebraic Geometry Over a Field of Characteristic One".

In the talk, I will present motivations, examples and some basic constructions of both theories, stressing their interrelations. http://en.wikipedia.org/wiki/Λ-ring

articles

• Thas, Koen. “Counting Points and Acquiring Flesh.” arXiv:1508.03997 [math], August 17, 2015. http://arxiv.org/abs/1508.03997.
• Thas, Koen. “A Taste of Weil Theory in Characteristic One.” arXiv:1507.06480 [math], July 23, 2015. http://arxiv.org/abs/1507.06480.