Related papers: A Class of Locally Complete Intersection Multiple …
A flat vector bundle on an algebraic variety supports two natural definable structures given by the flat and algebraic coordinates. In this note we show these two structures coincide, subject to a condition on the local monodromy at…
The aim of this note is to give a simple definition of genus zero virtual orientation classes (or fundamental classes) for projective complete intersections or, more generally, for complete intersections in convex varieties, and to prove a…
In this paper, we establish a new criterion for covering maps between real algebraic varieties. Specifically, we prove that a quasi-finite, flat morphism with locally constant geometric fibers between varieties over a real closed field…
We develop the theory of locally rigid and rigid symmetric monoidal $\infty$-categories over an arbitrary base $\mathcal{V}\in\mathrm{CAlg}(\mathbf{Pr}^\mathrm{L})$. Among other things, we prove that every locally rigid commutative…
In this paper, we explain a simple and uniform construction of a smooth integral model associated to a quadratic, (anti)-hermitian, and (anti)-quaternionic hermitian lattice defined over an arbitrary local field. As one major application,…
Motivated by the foundational result that a monomial complete intersection has the strong Lefschetz property (SLP) in characteristic zero, it is natural to ask when monomial almost complete intersections have the SLP. In this paper, using…
We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms. We show that with appropriate topologies each class of these…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…
Given a cover $\mathbb{U}$ of a family of smooth complex algebraic varieties, we associate with it a class $\mathcal{U},$ containing $\mathbb{U}$, of structures locally definable in an o-minimal expansion of the reals. We prove that the…
The algebraic structure of the integrable mixed mKdV/sinh-Gordon model is discussed and \textit{}extended to the AKNS/Lund-Regge model and to its corresponding supersymmetric versions. The integrability of the models is guaranteed from the…
We compute the compactly supported cohomology of the standard realization of any locally finite building.
Categorial methods for generating new local algebras from old ones are presented. A direct proof of the differential structure of the prolongations of a manifold is proposed.
In this paper we produce the first known formula for cohomologies of the derived tensor products of structure sheaves of subschemes in the case where the intersection of the subschemes is not a local complete intersection. The case covered…
We show that the group of type-preserving automorphisms of any irreducible semi-regular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated (abstractly)…
We extend our model for affine structures on toric Calabi-Yau hypersurfaces math.AG/0205321 to the case of complete intersections.
This is the first of a series of papers on the $L^2$-theory for formally integrable structures. It is devoted to constructing a resolution of the solution sheaf for a class of overdetermined systems introduced by L. H{\"o}rmander. A…
We investigate the homotopy type of a certain homogeneous space for a simple complex algebraic group. We calculate some of its classical topological invariants and introduce a new one. We also propose several conjectures about its…