Deninger then extended these results in various directions, such as non-torsion sheaves (1986), arithmetic surfaces (1987), as well as higher-dimensional local fields (with Wingberg, 1986).

In 1995, Deninger studied Massey products in Deligne cohomology and conjectured therefrom a formula for the special value for the L-function of an elliptic curve at s=3, which was subsequently confirmed by Goncharov (1996).

The Riemann ζ-function is defined using a product of Euler factors for each prime number p. In order to obtain a functional equation for ζ(s), one needs to multiply them with an additional term involving the Gamma function: More general L-functions are also defined by Euler products, involving, at each finite place, the determinant of the Frobenius endomorphism acting on l-adic cohomology of some variety X / Q, while the Euler factor for the infinite place are, according to Serre, products of Gamma functions depending on the Hodge structures attached to X / Q. Deninger (1991) expressed these Γ-factors in terms of regularized determinants and moved on, in 1992 and in greater generality in 1994, to unify the Euler factors of L-functions at both finite and infinite places using regularized determinants.

Among other properties, this site would be equipped with an action of R, and each prime number p would correspond to a closed orbit of the R-action of length log(p).

In 2010, Deninger proved that classical conjectures of Beilinson and Bloch concerning the intersection theory of algebraic cycles would be further consequences of his program.

In 2002, Deninger constructed a foliated space which corresponds to an elliptic curve over a finite field, and Hesselholt (2016) showed that the Hasse-Weil zeta-function of a smooth proper variety over Fp can be expressed using regularized determinants involving topological Hochschild homology.

It asserts that a vector bundle on a compact Riemann surface X is stable if it arises from a unitary representation of the fundamental group π1(X).

In Deninger & Werner (2005) established a p-adic analogue thereof: for a smooth projective algebraic curve over Cp, obtained by base change from

, they constructed an action of the etale fundamental group π1(X) on the fibers on certain vector bundles, including those of degree 0 and having potentially strongly semistable reduction.

In several joint papers, Deninger and Wilhelm Singhof studied quotients of the n-dimensional Heisenberg group H by the standard lattice consisting of integer-valued matrices, from various points of view.

In 1984, they computed the e-invariant of X in terms of ζ(−n), which leads to a construction of elements in the stable homotopy groups of spheres of arbitrarily large order.

The classical fact from Hodge theory that any cohomology class on a Kähler manifold admits a unique harmonic had been generalized by Álvarez López & Kordyukov (2001) to Riemannian foliations.

Deninger & Singhof (2001) show that foliations on the above space X, which satisfy only slightly weaker conditions, do not admit such Hodge theoretic properties.

Moreover, the logarithm of the Fuglede-Kadison determinant on the von Neumann algebra NΓ associated to Γ (which replaces the Mahler measure for Zn) agrees with the entropy of the above action.

In two papers around 2014, they simplified the theory by giving a presentation of the ring of Witt vectors in terms of a completion of the monoid algebra ZR.