Related papers: A comparison between obstructions to local-global …
For a complex analytic variety with an action of a finite group and for an invariant 1-form on it, we give an equivariant version (with values in the Burnside ring of the group) of the local Euler obstruction of the 1-form and describe its…
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
The Special Theory of Relativity and Quantum Mechanics merge in the key principle of Quantum Field Theory, the Principle of Locality. We review some examples of its ``unreasonable effectiveness'' (which shows up best in the formulation of…
We study local-global questions for Galois cohomology over the function field of a curve defined over a p-adic field (a field of cohomological dimension 3). We define Tate-Shafarevich groups of a commutative group scheme via cohomology…
The globalization problem arises when local tensor fields possess a given property (such as being symplectic or Poisson) but cannot be consistently extended to a global object due to incompatibilities on chart overlaps. A notable instance…
Let $K$ be the fraction field of a two-dimensional henselian, excellent, equi-characteristic local domain. We prove a local-global principle for Galois cohomology with finite coefficients over $K$. We use classical machinery from \'etale…
We study rational cuspidal curves in projective surfaces. We specify two criteria obstructing possible configurations of singular points that may occur on such curves. One criterion generalizes the result of Fernandez de Bobadilla, Luengo,…
<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted…
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or…
A complex projective manifold is rationally connected, resp. rationally simply connected, if finite subsets are connected by a rational curve, resp. the spaces parameterizing these connecting rational curves are themselves rationally…
We introduce in the framework of the linear approximation of General relativity a natural distinction between General gauge transformations generated by any vector field and those Special ones for which this vector field is a gradient. This…
For any number field, we prove that there exists a stacky curve of genus one half defined over the ring of its integers violating the local-global principle for integral points.
We consider the local to global principle for detecting linear dependence of points in groups of the Mordell-Weil type. As applications of our general setting we obtain corresponding statements for Mordell-Weil groups of non{-}CM elliptic…
As a starting point for higher-dimensional patching in the Berkovich setting, we show that this technique is applicable around certain fibers of a relative Berkovich analytic curve. As a consequence, we prove a local-global principle over…
In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main…
We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that…
The local and global interpretability of various ML models has been studied extensively in recent years. However, despite significant progress in the field, many known results remain informal or lack sufficient mathematical rigor. We…
We consider a local to global principle for detecting linear dependence of nontorsion points, by reduction maps, in the Mordell-Weil group of an abelian variety over a number field.
The framework of locally covariant quantum field theory is discussed, motivated in part using "ignorance principles". It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be…
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…