Related papers: Relative internality and definable fibrations
We investigate aspects of certain stringy invariants of singular elliptic fibrations which arise in engineering Grand Unified Theories in F-theory. In particular, we exploit the small resolutions of the total space of these fibrations…
Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…
Let p=tp(a/A) be a stationary type in an arbitrary finite rank stable theory, and P an A-invariant family of partial types. The following property is introduced and characterised: whenever c is definable over (A,a) and a is not algebraic…
Let $\mathcal{C}$ be an irreducible plane curve of $\text{PG}(2,\mathbb{K})$ where $\mathbb{K}$ is an algebraically closed field of characteristic $p\geq 0$. A point $Q\in \mathcal{C}$ is an inner Galois point for $\mathcal{C}$ if the…
In this paper we define a relative rigid fundamental group, which associates to a section $p$ of a smooth and proper morphism $f:X\rightarrow S$ in characteristic $p$, a Hopf algebra in the ind-category of overconvergent $F$-isocrystals on…
Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration with rationally connected fibers. We apply…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and…
The problem of equivariant rigidity is the $\Gamma$-homeomorphism classification of $\Gamma$-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of $\Gamma$. In other words, this is the…
The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact K\"ahler manifold with numerically trivial canonical bundle admits an \'etale cover that decomposes into a product of a torus, and irreducible,…
Galois comodules of a coring are studied. The conditions for a simple comodule to be a Galois comodule are found. A special class of Galois comodules termed principal comodules is introduced. These are defined as Galois comodules that are…
We prove that, for adic \'{e}tale motives over $\mathbb{C}_p$, the vector bundles on the Fargues-Fontaine curve arising from their Hyodo-Kato cohomology coincide with their de Rham-Fargues-Fontaine cohomologies, where the latter provides an…
This is a survey of recent examples of varieties that are not stably rational. We review the specialization method based on properties of the Chow group of zero-cycles used in these examples and explain the point of view of unramified…
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…
We give new sufficient conditions for the integrability and unique integrability of continuous tangent sub-bundles on manifolds of arbitrary dimension, generalizing Frobenius' classical Theorem for C^1 sub-bundles. Using these conditions we…
We introduce and study relatively divisible and relatively flat objects in exact categories in the sense of Quillen. For every relative cotorsion pair $(\mathcal{A},\mathcal{B})$ in an exact category $\mathcal{C}$, $\mathcal{A}$ coincides…
We apply our earlier work on the higher-dimensional analogue of the Mumford conjecture to two questions. Inspired by work of Ebert we prove non-triviality of certain characteristic classes of bundles of smooth closed manifolds. Inspired by…
The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a…
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
We describe two conjectures, one strictly stronger than the other, that give descriptions of the integral Bernstein center for GL_n(F) (that is, the center of the category of smooth W(k)[GL_n(F)]-modules, for F a p-adic field and k an…