相关论文: Descent for non-archimedean analytic spaces

In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are modelled on a finite…

This work brings to light some partial \emph{anabelian behaviours} of analytic annuli in the context of Berkovich geometry. More specifically, if $k$ is a valued non-archimedean complete field of mixed characteristic which is algebraically…

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…

We present a new construction of gradient-like vector fields in the setting of Morse theory on a complex analytic stratification. We prove that the ascending and descending sets for these vector fields possess cell decompositions satisfying…

Double descent is a method to construct automorphic representations of classical groups. For given A-parameter $\psi$ with certain good properties, double descent constructs a space of functions orthogonal to any cuspidal representation…

We describe quasi-Hopf twist deformations of flat closed string compactifications with non-geometric R-flux using a suitable cochain twist, and construct nonassociative deformations of fields and differential calculus. We report on our new…

This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp boundedness of almost diagonal operators on matrix-weighted…

We consider gradient descent with constant stepsizes and derive exact worst-case convergence rates on the minimum gradient norm of the iterates. Our analysis covers all possible stepsizes and arbitrary upper/lower bounds on the curvature of…

`Double descent' delineates the generalization behaviour of models depending on the regime they belong to: under- or over-parameterized. The current theoretical understanding behind the occurrence of this phenomenon is primarily based on…

The quotient shape types of normed vectorial spaces(over the same field) with respect to Banach spaces reduce to those of Banach spaces. The finite quotient shape type of normed spaces is an invariant of the (algebraic) dimension, but not…

We show that, for Finsler spaces with cubic metric, Landsberg spaces are Berwaldian. Also, for decomposable metrics, we determine specific conditions for a space with cubic metric to be of Berwald type, thus refining the result in [6].

Discussed is mechanics of objects with internal degrees of freedom in generally non-Euclidean spaces. Geometric peculiarities of the model are investigated detailly. Discussed are also possible mechanical applications, e.g., in dynamics of…

Despite recent theoretical progress on the non-convex optimization of two-layer neural networks, it is still an open question whether gradient descent on neural networks without unnatural modifications can achieve better sample complexity…

We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four…

We extend coordinate descent to manifold domains, and provide convergence analyses for geodesically convex and non-convex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and…

We introduce the use of $p$-descent techniques for elliptic surfaces over a perfect field of characteristic not $2$ or $3$. Under mild hypotheses, we obtain an upper bound for the rank of a non-constant elliptic surface. When $p=2$, this…

Since their inception perfectoid spaces have catalyzed a revolution in p-adic geometry. We redevelop the foundations of perfectoid spaces from the point of view of Berkovich Spaces, where the underlying topological space of an affinoid…

In this note, we consider two types of estimates for the Harnack distance in bounded domains of a finite-dimensional Euclidean space. The first type is based on the geometric concept of the entropy of arcwise connectedness. We used this…

We study multidimensional cosmological models with a higher-dimensional product manifold, that consists of spherical and flat spaces, in the presence of a minimal free scalar field. Dynamical behaviour of the model is analyzed both in…

We develop the general theory of \emph{topometric spaces}, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric function. Spaces of global and local types in continuous logic are the motivating examples for the…