Lefschetz trace formula for open adic spaces

SCALING GROUP FLOW AND LEFSCHETZ TRACE FORMULA FOR LAMINATED SPACES WITH p−ADIC TRANSVERSAL

In his approach to analytic number theory C. Deninger has suggested that to the Riemann zeta function ζ̂(s) (resp. the zeta function ζY (s) of a smooth projective curve Y over a finite field Fq, q = p f )) one could possibly associate a foliated Riemannian laminated space (SQ,F , g, φ) (resp. (SY ,F , g, φ)) endowed with an action of a flow φ whose primitive compact orbits should correspond to t...

The Grothendieck-Lefschetz trace formula

We caution that # Fix(ψ) has to be interpreted with some care: it really denotes a fixed point count with multiplicities. A better way to phrase it as follows. Inside M ×M we have two submanifolds: the diagonal ∆ and the graph Γψ. We can then try to take # Fix(ψ) := ∆ · Γψ = “intersection number of ∆ and Γψ”. When ∆ and Γψ intersect transversely this intersection number coincides with the naïve...

A conjectural Lefschetz formula for locally symmetric spaces

A Lefschetz formula for flows

We want to formulate an analogous statement for a flow Φ instead of a diffeomorphism. By looking at the local side of (1) the first idea would be to consider the fixed points of the flow and to assume they are nondegenerate. This way we get the Hopf formula expressing the Euler characteristic on the global side. More subtle information is supposed to be obtained by considering the closed orbits...

The Trace Formula in Banach Spaces

A classical result of Grothendieck and Lidskii says that the trace formula (that the trace of a nuclear operator is the sum of its eigenvalures provided the sequence of eigenvalues is absolutely summable) holds in Hilbert spaces. In 1988 Pisier proved that weak Hilbert spaces satisfy the trace formula. We exhibit a much larger class of Banach spaces, called Γ-spaces, that satisfy the trace form...