Related papers: Topological behaviour of logarithmic invariants

Let $\Lambda \subset \mathbb R^n$ be an algebraic lattice, coming from a projective module over the ring of integers of a number field $K$. Let $\mathcal Z \subset \mathbb R^n$ be the zero locus of a finite collection of polynomials such…

Commutative $d$-torsion $K$-theory is a variant of topological $K$-theory constructed from commuting unitary matrices of order dividing $d$. Such matrices appear as solutions of linear constraint systems that play a role in the study of…

We study the category whose objects are graphs of fixed genus and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian and we study two families of modules over these categories.…

Let $K$ be an algebraic number field with ring of integers $\Cal{O}_{K}$, $p>2$ be a rational prime and $G$ be the cyclic group of order $p $. Let $\Lambda$ denote the order $\Cal{O}_{K}[G].$ Let $Cl(\Lambda)$ denote the locally free class…

We establish the Lyndon interpolation property for basic lattice expansion logics (LE-logics) in arbitrary signatures using display calculi. Our approach is constructive, yielding interpolants algorithmically from derivations, and modular,…

Let G be a torus and M a G-Hamiltonian manifold with Kostant line bundle L and proper moment map. Let P be the weight lattice of G. We consider a parameter k and the multiplicity $m(\lambda,k)$ of the quantized representation associated to…

For a closed Riemannian manifold we extend the definition of analytic and Reidemeister torsion associated to an orthogonal representation of fundamental group on a Hilbert module of finite type over a finite von Neumann algebra. If the…

We define an extended Bloch group for an arbitrary field F, and show that this group is canonically isomorphic to K_3^ind(F) if F is a number field. This gives an explicit description of K_3^ind(F) in terms of generators and relations. We…

We introduce a twisted version of $K$-theory with coefficients in a $C^*$-algebra $A$, where the twist is given by a new kind of gerbe, which we call Morita bundle gerbe. We use the description of twisted $K$-theory in the torsion case by…

For a smooth manifold X of dimension <d we construct a homomorphism from the algebraic K-theory group in degree d of the algebra of smooth functions on X to the degree -d-1 topological K-theory of X with coefficients in C/Z. This map…

Let $K$ be a field finitely generated over the field of rational numbers, $K(c)$ the extension of $K$ obtained by adjoining all roots of unity, $L$ an infinite Galois extension of $K$, $X$ an abelian variety defined over $K$. We prove that…

Let $\mathbb{C}_q$ be a non-commutative Laurent polynomial ring associated with a $(n+1)\times (n+1)$ rational quantum matrix $q$. Let $\mathfrak{sl}_d(\mathbb{C}_q)\oplus HC_1(\mathbb{C}_q)$ be the universal central extension of Lie…

For a Noetherian $R$-algebra $\Lambda$, there is a canonical inclusion $\mathsf{tors}\Lambda\to\prod_{\mathfrak{p}\in \mathrm{Spec} R}\mathsf{tors}(\kappa(\mathfrak{p})\Lambda)$, and each element in the image satisfies a certain…

Let $E_{d}(\ell)$ denote the space of all closed $n$-gons in $\R^{d}$ (where $d\ge 2$) with sides of length $\ell_1,..., \ell_n$, viewed up to translations. The spaces $E_d(\ell)$ are parameterized by their length vectors $\ell=(\ell_1,...,…

Let $p$ be a prime number, let $K$ be a $p$-field (a local field with finite residue field of characteristic $p$), let $L$ be a finite galoisian tamely ramified extension of $K$, and let $G=\mathrm{Gal}(L|K)$. Suppose that $L$ is split over…

We study the category whose objects are trees (with or without roots) and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian, and we study two natural families of modules over…

We show that Riemann-Hurwitz-style translation formulas obtained by Kuz'min, Kida, Iwasawa, Wingberg et alii for the lambda invariant attached to certain Iwasawa moduli in cyclotomic Z{\ell}-extension of number fields are essentially…

We consider the (direct sum over all $n$ of the) $K$-theory of the semi-nilpotent commuting variety of $\mathfrak{gl}_n$, and describe its convolution algebra structure in two ways: the first as an explicit shuffle algebra (i.e. a…

We refine the invariant on $K_2(A[C_{p_e}]/I_m,(T-1))$ constructed in a previous paper to one which is an isomorphism for all $\lambda$-rings $A$.

We fix a prime number $p$ and $\K$ a number field, we denote by $M$ the maximal abelian $p$-extension of $\Ko$ unramified outside $p$. The aim of this paper is to study the $\Z_p$-module $\gal(M/\Ko)$ and to give a method to effectively…