Results 1 
2 of
2
Lectures on graded differential algebras and noncommutative geometry
, 1999
"... These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments. ..."
Abstract

Cited by 49 (5 self)
 Add to MetaCart
(Show Context)
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments.
Schemes over F1 and Zeta Functions
, 2009
"... We determine the real counting function N(q) (q ∈ [1, ∞)) for the hypothetical “curve” C = Spec Z over F1, whose corresponding zeta function is the complete Riemann zeta function. Then, we develop a theory of functorial F1schemes which reconciles the previous attempts by C. Soulé and A. Deitmar. ..."
Abstract
 Add to MetaCart
(Show Context)
We determine the real counting function N(q) (q ∈ [1, ∞)) for the hypothetical “curve” C = Spec Z over F1, whose corresponding zeta function is the complete Riemann zeta function. Then, we develop a theory of functorial F1schemes which reconciles the previous attempts by C. Soulé and A. Deitmar. Our construction fits with the geometry of monoids of K. Kato, is no longer limited to toric varieties and it covers the case of schemes associated to Chevalley groups. Finally we show, using the monoid of adèle classes over an arbitrary global field, how to apply our functorial theory of Moschemes to interpret conceptually the spectral realization of zeros of Lfunctions.