(non)commutative f-un geometry

Abstract

Stressing the role of dual coalgebras, we modify the definition of affine schemes over the 'field with one element'. This clarifies the appearance of Habiro-type rings in the commutative case, and, allows a natural noncommutative generalization, the study of representations of discrete groups and their profinite completions being our main motivation.

References in corpus (4)

• Cyclotomy and analytic geometry over F_1
• On the notion of geometry over $\F_1$
• Noncommutative geometry and dual coalgebras
• Noncommutative Tangent Cones and Calabi Yau Algebras