In mathematics, the Riemann-Hilbert correspondence is a generalization of Hilbert's twenty-first problem to higher dimensions. The original setting was for Riemann surfaces, where it was about the existence of regular differential equations with prescribed monodromy groups. In higher dimensions, ...
This is a survey paper on the Riemann-Hilbert correspondence on (irregular) holonomic D-modules, based on the 16-th Takagi lecture (2015/11/28). In this paper, we use subanalytic sheaves, an analogous notion to the one of indsheaves. 关键词: Mathematics - Algebraic Geometry DOI: 10.4855...
on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection on its “base change to {\mathrm {B}}_{{\text {dR}}}”, which can be regarded as a first step towards the sought-after p-adic Riemann–Hilbert correspondence. As...
arXiv:1610.00540v2 [math.KT] 12 Oct 2016K-THEORY OF SEMI-LINEAR ENDOMORPHISMS VIA THERIEMANN–HILBERT CORRESPONDENCEOLIVER BRAUNLINGAbstract. Grayson, developing ideas of Quillen, has made computations of the K-theory of ‘semi-linear endomorphisms’. In the present text we develop a techniqueto...
Riemann-Hilbert correspondenceThe geometric phase that appears in the effects of Aharonov–Bohm type is interpreted in the frame of Deligne's version of the Riemann–Hilbert correspondence. We extend also the concept of flat gauge field to B-branes on a complex manifold X, so that such a ...
We construct a natural infinity-categorical equivalence between these two categories generalising the classical Riemann-Hilbert correspondence.doi:10.48550/arXiv.1308.5890Alexander PaulinMathematicsA. Paulin, The Riemann-Hilbert Correspondence for Algebraic Stacks, 1308.5890, 2013....
The Higher Riemann-Hilbert Correspondence and Multiholomorphic MappingsAaron Smith
Riemann-Hilbert correspondenceHomotopy-coherent representationsTwisting cochainsWe construct an A∞-quasi-equivalence of dg-categories between PA — the category of prefect A0-modules with flat Z-connection, associated to the de Rham dga A of a compact manifold M — and the dg-category of infinity...
doi:10.1142/9789814271219_0006MarcolliMatildeAlain Connes, Matilde Marcolli Renormalization, the Riemann-Hilbert correspondence, and motivic Galois theory Frontiers in number theory, physics, and geometry (II) Springer, Berlin (2007) 617-713.
Then, we put the problem of inverting the re-scaled operator associated with \\(\\mathcal {S}_{N;\\gamma }\\) in correspondence with a vector valued Riemann-Hilbert problem. The resolution of this vector problem demands the resolution of a \\(2imes 2\\) matrix Riemann鈥揌ilbert ...