相关论文: On arithmetic models and functoriality of Bost-Con…
We show that the algebra and the endomotive of the quantum statistical mechanical system of Bost--Connes naturally arises by extension of scalars from the "field with one element" to rational numbers. The inductive structure of the abelian…
In this note, using Borger's theory of periodic Witt vectors, we construct integral refinements of the arithmetic subalgebras associated with Bost-Connes systems for general number fields.
We consider a Hecke algebra naturally associated with the affine group with totally positive multiplicative part over an algebraic number field K and we show that the C*-algebra of the Bost-Connes system for K can be obtained from our Hecke…
We compare two different models of noncommutative geometry of the cyclotomic tower, both based on an arithmetic algebra of functions of roots of unity and an action by endomorphisms, the first based on the Bost-Connes quantum statistical…
Associated to a simple root of a finite-dimensional complex semisimple Lie algebra, there are several endofunctors (defined by Arkhipov, Enright, Frenkel, Irving, Jantzen, Joseph, Mathieu, Vogan and Zuckerman) on the BGG category…
It was recently shown [2] that the resolvent algebra of a non-relativistic Bose field determines a gauge invariant (particle number preserving) kinematical algebra of observables which is stable under the automorphic action of a large…
In this thesis we compare V. Voevodsky's geometric motives to the derived category of M. Nori's abelian category of mixed motives by constructing a triangulated tensor functor between them. It will be compatible with the Betti realizations…
The classification problem of Bost-Connes systems was studied by Cornellissen and Marcolli partially, but still remains unsolved. In this paper, we will give a representation-theoretic approach to this problem. We generalize the result of…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
The aim of this project is to attach a geometric structure to the ring of integers. It is generally assumed that the spectrum $\mathrm{Spec}(\mathbb{Z})$ defined by Grothendieck serves this purpose. However, it is still not clear what…
For a graph $E$, we introduce the notion of an extended $E$-algebraic branching system, generalising the notion of an $E$-algebraic branching system introduced by Gon\c{c}alves and Royer. We classify the extended $E$-algebraic branching…
After the language of module and theirs morphisms, this short course presents matricial calculus and determinants in a commutative ring as appliction of ``remarquable identities'' in the ring of polynomials with integer coefficients with…
We introduce a systematic framework for counting and finding independent operators in effective field theories, taking into account the redundancies associated with use of the classical equations of motion and integration by parts. By…
Each number field has an associated finite abelian group, the class group, that records certain properties of arithmetic within the ring of integers of the field. The class group is well-studied, yet also still mysterious. A central…
Bezrukavnikov and Etingof introduced some functors between the categories O for rational Cherednik algebras. Namely, they defined two induction functors Ind_b, ind_\lambda and two restriction functors Res_b,res_\lambda. They conjectured…
By using the theory of Complex Multiplication for general Siegel modular varieties we construct arithmetic subalgebras for BC-type systems attached to number fields containing a CM field. Our approach extends the construction of Connes,…
We focus on the continuous symmetry transformations for the three ($2 + 1$)-dimensional (3D) system of a combination of the free Abelian 1-form and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We…
The perturbative expansion of tensorial field theories in Feynman graphs can be interpreted as weighted generating series of some piecewise linear varieties. This simple fact establishes a link between two a priori distinct fields: the…
With a global function field K with constant field F_q, a finite set S of primes in K and an abelian extension L of K, finite or infinite, we associate a C*-dynamical system. The systems, or at least their underlying groupoids, defined…
We show that taking the set of primitive idempotents of commutative association schemes is a functor from the category of commutative association schemes with surjective morphisms to the category of finite sets with surjective partial…