相关论文: Invitation to higher local fields, Part II, sectio…
For a group $G$, we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflect various properties of the group orderings.
The recently developed 3D graphic statics (3DGS) lacks a rigorous mathematical definition relating the geometrical and topological properties of the reciprocal polyhedral diagrams as well as a precise method for the geometric construction…
Starting from Gau{\ss}' and Legendre's quadratic reciprocity law we want to sketch how it gave rise to the development of higher and generalized reciprocity laws and over all explicit reciprocity formulas in Iwasawa theory.
We give a new construction of linear codes over finite fields on higher dimensional varieties using Grothendieck's theory of residues. This generalizes the construction of differential codes over curves to varieties of higher dimensions.
A "reduced" differential geometry adapted to the presence of abelian isometries is constructed.Classical T-duality diagonalizes in this setting, allowing us to get conveniently the transformation of the relevant geometrical objects such as…
B. Xu characterized rank $4$ self-dual association schemes inducing three partial geometric designs by their character tables. We construct such association schemes as Schur rings over abelian $2$-groups.
We explicitly study Kato's residue homomorphisms in Milnor $K$-theory, which are closely related to Contou-Carr\`ere symbols. As applications we establish several reciprocity laws for certain locally defined maps on $K$-groups that are…
We associate to a full flag $\mathcal{F}$ in an $n$-dimensional variety $X$ over a field $k$, a "symbol map" $\mu_{\mathcal{F}}:K(F_X) \to \Sigma^n K(k)$. Here, $F_X$ is the field of rational functions on $X$, and $K(\cdot)$ is the…
The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the…
The right near-domain is defined to loosen near-domain axioms. Correspondence of a class of the right near-domains and a class of sharply 2--transitive groups is constructed.
It is proved that the members of the Riccati hierarchy, the so-called Riccati chain equations, can be considered as particular cases of projective Riccati equations, which greatly simplifies the study of the Riccati hierarchy. This also…
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…
Parshin's higher Witt pairing on an arithmetic surface can be combined with the higher tame pairing to form a symbol taking values in the absolute abelian Galois group of the function field. We prove reciprocity laws for this symbol using…
We solve a technical problem related to adeles on an algebraic surface. Given a finite set of natural numbers up to two, one associates an adelic group. We show that this operation commutes with taking intersections if the surface is…
With the help of Wick rotation over $p$-adic numbers $\mathbb{Q}_p$, the $p$-adic version of Euclidean $\textrm{dS}_2$ space(noted as $p\textrm{dS}_2$) is obtained based on $p\textrm{AdS}_2$($p$-adic version of Euclidean $\textrm{AdS}_2$…
In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture…
We develop a formalism of cohomological descent encoding adelic points and obstructions to local-global principle on algebraic stacks. As an application, by constructing new obstructions using the formalism, we obtain some comparison…
In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using these results we construct algebraic-geometric codes which…
The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…
We prove a conjecture of Bhatt-Hansen that derived pushforwards along proper morphisms of rigid-analytic spaces commute with Verdier duality on Zariski-constructible complexes. In particular, this yields duality statements for the…