N oncommutative geometry, in the sense in which this book uses the term, is to a very large
extent the creation of a single mathematician, Alain Connes. Chapter 3, indeed, begins with …

The Riemann hypothesis is, and will hopefully remain for a long time, a great motivation to
uncover and explore new parts of the mathematical world. After reviewing its impact on the …

We consider the Tate cohomology of the circle group acting on the topological Hochschild
homology of schemes. We show that in the case of a scheme smooth and proper over a …

Text We show that the basic categorical concept of an S-algebra as derived from the theory
of Segal's Γ-sets provides a unifying description of several constructions attempting to model …

We report on the following highlights from among the many discoveries made in
Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the …

The Strong Künneth Theorem for Topological Periodic Cyclic Homology Page 1 Number 1508 The
Strong Kunneth Theorem for Topological Periodic Cyclic Homology Andrew J. Blumberg Michael …

Segal's Γ-rings provide a natural framework for absolute algebraic geometry. We use G.
Almkvist's global Witt construction to explore the relation with J. Borger-geometry and …

The first part of this note shows that the odd-period polynomial of each Hecke cusp
eigenform for the full modular group produces via the Rodriguez-Villegas transform ([1]) a …

Noncommutative geometry has its roots both in quantum physics and in pure mathematics.
One of its main themes is to explore and investigate “new spaces” that lie beyond the scope …

Given a point p of the topos Δ ˆ of simplicial sets and the corresponding flat covariant functor
F: Δ⟶ Sets, we determine the extensions of F to the cyclic category Λ⊃ Δ. We show that to …