Related papers: To the multidimensional tame symbol
The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the…
For smooth linear group schemes over $\bbZ$ we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa measures for motives defined by Bloch and Kato. We show that…
We survey explicit coordinate descriptions for two (A and X) versions of Teichmuller and lamination spaces for open 2D surfaces, and extend them to the more general set-up of surfaces with distinguished collections of points on the…
We note that two formulations of dual gonihedric Ising models in 3d, one based on using Wegner's general framework for duality to construct a dual Hamiltonian for codimension one surfaces, the other on constructing a dual Hamiltonian for…
We prove the strong Tits alternative for the 3-dimensional tame automorphism group over a field K of characteristic zero.
We develop the theory of linear algebra over a (Z_2)^n-commutative algebra (n in N), which includes the well-known super linear algebra as a special case (n=1). Examples of such graded-commutative algebras are the Clifford algebras, in…
We prove an A'Campo type formula for the tame monodromy zeta function of a smooth and proper variety over a discretely valued field $K$. As a first application, we relate the orders of the tame monodromy eigenvalues on the $\ell$-adic…
We prove the following group analogue of the well-known Heyde theorem on a characterization of the Gaussian distribution on the real line. Let $X$ be a second countable locally compact Abelian group containing no subgroups topologically…
We consider a complex of tori of length 2 defined over a number field k. We establish here some local and global duality theorems for the (\'etale or Galois) hypercohomology of such a complex. We prove the existence of a Poitou-Tate exact…
In 1991, Rousseau gave a new proof of Gauss's quadratic reciprocity by comparing two distinct coset representations of the group $(\mathbb{Z}_{p}^{*} \times \mathbb{Z}_{q}^{*}) / U$ using the Chinese Remainder Theorem, without Gauss's…
In this paper we will consider noncommutativity that arises from bosonic T-dualization of type II superstring in presence of Ramond-Ramond (RR) field, which linearly depends on the bosonic coordinates $x^\mu$. The derivative of the RR field…
Tate gave a famous construction of the residue symbol on curves by using some non-commutative operator algebra in the context of algebraic geometry. We explain Beilinson's multidimensional generalization, which is not so well-documented in…
We show that dualising transfer maps in Hochschild cohomology of symmetric algebras commutes with Tate duality. This extends a well-known result in group cohomology.
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools are based on the well-known de Rham-Kodaira decomposing theorem on harmonic…
We analyse the Gauss-Manin system of differential equations---and its Fourier transform---attached to regular functions satisfying a tameness assupmption on a smooth affine variety over C (e.g. tame polynomials on C^{n+1}). We give a…
We explore type II supersymmetric double field theory in superspace. The double supervielbein is an element of the orthosymplectic group OSp(10,10|64), which also governs the structure of generalized superdiffeomorphisms. Unlike bosonic…
Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected…
We study the $l$-adic cohomology of unramified Rapoport-Zink spaces of EL-type. These spaces were used in Harris and Taylor's proof of the local Langlands correspondence for $\mathrm{GL_n}$ and to show local-global compatibilities of the…
In this work, on the one hand, we survey and amplify old results concerning tame dynamical systems and, on the other, prove some new results and exhibit new examples of such systems. In particular, we study tame symbolic systems and…
We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…