Related papers: $K$-theoretic torsion and the zeta function
Using ideas from algebraic topology and statistical mechanics, we generalize Kirchhoff's network and matrix-tree theorems to finite CW complexes of arbitrary dimension. As an application, we give a formula expressing Reidemeister torsion as…
We describe the algebraic K-theory of the $K(1)$-local sphere and the category of type 2 finite spectra in terms of K-theory of discrete rings and topological cyclic homology. We find an infinite family of 2-torsion classes in the $K_0$ of…
The theta characteristics on a Riemann surface are permuted by the induced action of the automorphism group, with the orbit structure being important for the geometry of the curve and associated manifolds. We describe two new methods for…
Using the cohomology theory of Dwork, as developed by Adolphson and Sperber, we exhibit a deterministic algorithm to compute the zeta function of a nondegenerate hypersurface defined over a finite field. This algorithm is particularly…
Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Corti\~nas et al. who calculated the K-theory of, in addition to…
We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…
This is a survey on Reidemeister torsion for hyperbolic three-manifolds of finite volume. Torsions are viewed as topological invariants and also as functions on the variety of representations in $\operatorname{ SL}_2(\mathbb C)$. In both…
Placing a Dirac-Schr\"odinger operator along the orbit of a flow on a compact manifold \(M\) defines an \(\R\)-equivariant spectral triple over the algebra of smooth functions on \(M\). We study some of the properties of these triples,…
Any $\mathbb{N}$-graded commutative Gorenstein ring $R$ of Krull dimension one with $R_0$ a field admits a standard silting object $V$ in the stable category $\underline{\mathrm{CM}}_0^{\mathbb{Z}}R$, and the object $V$ is tilting if and…
The higher rank Lefschetz formula for p-adic groups is used to prove rationality of a several-variable zeta function attached to the action of a p-adic group on its Bruhat-Tits building. By specializing to certain lines one gets…
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…
The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given…
We define a $K$-theory for pointed right derivators and show that it agrees with Waldhausen $K$-theory in the case where the derivator arises from a good Waldhausen category. This $K$-theory is not invariant under general equivalences of…
A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different…
Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of…
The (Iwahori-)Hecke algebra in the title is a $q$-deformation $\sH$ of the group algebra of a finite Weyl group $W$. The algebra $\sH$ has a natural enlargement to an endomorphism algebra $\sA=\End_\sH(\sT)$ where $\sT$ is a $q$-permutation…
Let $K[HK_{\Theta}]$ denote the Hecke-Kiselman algebra of a finite oriented graph $\Theta$ over an algebraically closed field $K$. All irreducible representations, and the corresponding maximal ideals of $K[HK_{\Theta}]$, are characterized…
We give a number field analogue of a result of Ramanujan, Hardy and Littlewood, thereby obtaining a modular relation involving the non-trivial zeros of the Dedekind zeta function. We also provide a Riesz-type criterion for the Generalized…
The paper studies the $K$-theoretic invariants of the crossed product $C^{*}$-algebras associated with an important family of homeomorphisms of the tori $\Bbb{T}^{n}$ called {\em Furstenberg transformations}. Using the Pimsner-Voiculescu…
Let $E$ be an elliptic curve defined over $\mathbb{Q}$. In this article, we classify all groups that can arise as $E(\mathbb{Q}(\zeta_p))_{\text{tors}}$ up to isomorphism for any prime $p$. When $p - 1$ is not divisible by small integers…