Related papers: Patching over Analytic Fibers and the Local-Global…

We prove a certain non-linear version of the Levi extension theorem for meromorphic functions. This means that the meromorphic function in question is supposed to be extendable along a sequence of complex curves, which are arbitrary, not…

This article proves the existence of a bound on the sum of local Betti numbers of a real analytic germ by a polynomial function of its multiplicity. This result can be interpreted as a localization of the classical Oleinik-Petrovsky bound…

We define and investigate a family of local-global principles for fields involving both orderings and p-valuations. This family contains the PAC, PRC and PpC fields and exhausts the class of pseudo classically closed fields. We show that…

We introduce a site-wise domination criterion for local percolation models, which enables the comparison of one-arm probabilities even in the absence of stochastic domination. The method relies on a local-to-global principle: if, at each…

In this thesis we investigate a new formalism for supergeometry which focuses on the categorical properties of the theory. This approach is our main tool in the subsequent investigation of a global analytic approach to the construction of…

We investigate the topological properties of Berkovich analytifications over hybrid fields, that is a field equipped with the maximum of its native norm and the trivial norm. We prove that the analytification of the affine line or of a…

We define a notion of global analytic space with overconvergent structure sheaf. This gives an analog on a general base Banach ring of Grosse-Kloenne's overconvergent p-adic spaces and of Bambozzi's generalized affinoid varieties over R.…

Suppose that a complex manifold M is locally embedded into a higher-dimensional neighbourhood as a submanifold. We show that, if the local neighbourhood germs are compatible in a suitable sense, then they glue together to give a global…

Although Berkovich spaces may fail to be metrizable when defined over too big a field, we prove that a large part of their topology can be recovered through sequences: for instance, limit points of subsets are actual limits of sequences and…

We propose a decentralised "local2global" approach to graph representation learning, that one can a-priori use to scale any embedding technique. Our local2global approach proceeds by first dividing the input graph into overlapping subgraphs…

We consider local-global principles for rational points on varieties, in particular torsors, over one-variable function fields over complete discretely valued fields. There are several notions of such principles, arising either from the…

In this paper and its sequel we consider locally-free $\mathscr{O}_X$-modules together with a connection over a quasi-smooth Berkovich curve $X$. We obtain necessary and sufficient conditions for the finite dimensionality of their de Rham…

We prove that the Berkovich space of the algebra of bounded analytic functions on the open unit disk of an algebraically closed nonarchimedean field contains multiplicative seminorms that are not norms and whose kernel is not a maximal…

We prove that every one-dimensional locally normal metric current, intended in the sense of U. Lang and S. Wenger, admits a nice integral representation through currents associated to (possibly unbounded) curves with locally finite length,…

Tempered ultra-hyperfunctions do not have the same type of localization properties as Schwartz distributions or Sato hyperfunctions; but the localization properties seem to play an important role in the proofs of the various versions of the…

We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…

In this article, we discuss the semicontinuity problem of certain properties on fibers for a morphism of schemes. One aspect of this problem is local. Namely, we consider properties of schemes at the level of local rings, in which the main…

Over the past two decades, many studies in the Density Functional Theory context revealed new aspects and properties of strongly correlated superfluid quantum systems in numerous configurations that can be simulated in experiments. This was…

We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested.…

We prove the failure of the local-global principle, with respect to discrete valuations, for isotropy of quadratic forms over function fields of transcendence degree at least 2 over algebraically closed fields. Our construction involves…