Remarks on zeta functions and K-theory over \mathbf F₁

2006/11/01 by Anton Deitmar · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Affine transformation #Mathematics #Pure mathematics #Field (mathematics) #Element (criminal law) #Group (periodic table) #Mathematical physics #Algebra over a field #Physics #Quantum mechanics

paper · pdf · doi:10.3792/pjaa.82.141

openalex publication_date 2006/11/01 · openalex created_date 2017/10/27 · openalex updated_date 2025/11/06

Abstract

We show that the notion of zeta functions over the field of one element \F₁, as given in special cases by Soulé, extends naturally to all \F₁-schemes as defined by the author in an earlier paper. We further give two constructions of K-theory for affine schemes or \F₁-rings, we show that these coincide in the group case, but not in general.

Citations

• Higher algebraic K-theory: I

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