Related papers: Adelic solenoid I: Structure and topology

Let X be a smooth complex algebraic variety with the Zariski topology, and let Y be the underlying complex manifold with the complex topology. Grothendieck's algebraic de Rham theorem asserts that the singular cohomology of Y with complex…

To the integral symplectic group Sp(2g,Z) we associate two posets of which we prove that they have the Cohen-Macaulay property. As an application we show that the locus of marked decomposable principally polarized abelian varieties in the…

We work with completed adelic structures on an arithmetic surface and justify that the construction under consideration is compatible with Arakelov geometry. The ring of completed adeles is algebraically and topologically self-dual and…

We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$,…

Let X be a variety over a field of characteristic 0. Given a vector bundle E on X we construct Chern forms c_{i}(E;\nabla) in \Gamma(X, \cal{A}^{2i}_{X}). Here \cal{A}^{.}_{X} is the sheaf Beilinson adeles and \nabla is an adelic…

We study projectively flat holomorphic vector bundles over Riemann surfaces. To each such bundle, we naturally assign a Wronskian line bundle. The main idea is a notion of the division of two meromorphic sections. Abel's identity is…

A large variety of cohomology theories is derived from complex cobordism MU^*(-) by localizing with respect to certain elements or by killing regular sequences in MU_*. We study the relationship between certain pairs of such theories which…

We consider the interplay of point counts, singular cohomology, \'etale cohomology, eigenvalues of the Frobenius and the Grothendieck ring of varieties for two families of varieties: spaces of rational maps and moduli spaces of marked,…

We study the topological structure of the symmetry group of the standard model, $G_{SM}=U(1)\times SU(2)\times SU(3)$. Locally, $G_{SM}\cong S^1\times (S^3)^2\times S^5$. For SU(3), which is an $S^3$ bundle over $S^5$ (and therefore a local…

We investigate the geometry of a certain space of meromorphic connections with irregular singularities, and prove in particular that it is a (real) symplectic Lie groupoid. The connections have a physical meaning: they correspond to certain…

We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy…

We are interested in the geometry of the group $\mathcal{D}_q(M)$ of diffeomorphisms preserving a contact form $\theta$ on a manifold $M$. We define a Riemannian metric on $\mathcal{D}_q(M)$, compute the corresponding geodesic equation, and…

This paper concerns the topology of the isospectral {\it real} manifold of the ${\mathfrak sl}(N)$ periodic Toda lattice consisting of $2^{N-1}$ different systems. The solutions of those systems contain blow-ups, and the set of those…

Let $G$ denote a linear algebraic group over $\mathbf{Q}$ and $K$ and $L$ two number fields. Assume that there is a group isomorphism of points on $G$ over the finite adeles of $K$ and $L$, respectively. We establish conditions on the group…

Given a finite morphism $\varphi:Y\to X$ of quasi-smooth Berkovich curves over a complete, algebraically closed field $k$ of characteristic $0$, we prove a Riemann-Hurwitz formula relating their Euler-Poincar\'e characteristics (calculated…

It is shown that the groups of automorphisms of Euclidean spaces are isomorphic to the groups of topologic automorphisms of respectively factored arithmetic spaces. In particular, the geometry of Euclidean n-space with positive signature is…

Extending [14], we obtain a complete description of the motivic cohomology with ${\mathbb Z}/2$-coefficients of the Nisnevich classifying space of the spin group $Spin_n$ associated to the standard split quadratic form. This provides us…

We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational…

We study geodesics on hypersurfaces close to the standard (n-1)-dimensional sphere in n-dimensional Euclidean space. Following Poincar\'e, we treat the problem within the framework of the analytical mechanics, and employ the perturbation…

Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components $M_{DH}^d(X,G)$ and $M_{DH}^{d'}(X',G')$ of the associated Deligne--Hitchin…