The monodromy theorem
WebSo in complex analysis, the Monodromy Theorem says that: Let $\gamma_0,\gamma_1$ be two paths in $\mathbb C$ s.t $\gamma_0(0)=\gamma_1(0)=a$ and $\gamma_0(1)=\gamma_1(1)=b$ . Let $\{\gamma_s\}_{s\in[0,1]}$ be a homotopy between $\gamma_0$ and $\gamma_1$ fixing the end points. WebOct 12, 2024 · Tau function and generating function of the monodromy map. The above theorem allows to establish the relationship between the isomonodromic tau-function and the generating function of the monodromy map. Namely, consider some local symplectic potential \(\theta _{\mathcal {M}}\) for the form \(\omega _{\mathcal {M}}\) such that
The monodromy theorem
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Web1) The monodromy group of a topological space. 2) The ℓ -adic monodromy theorem of Grothendieck. 3) The p -adic monodromy conjecture of Fontaine (which is now proved). I … WebFeb 20, 2014 · 2. The simplest situation is when your fibration is actually a covering space and the simplest nontrivial covering space is given by f: S 1 → S 1 where f ( z) = z 2. Roughly speaking this map wraps the upstairs (domain) circle around the downstairs (target) circle twice. If you start from any point downstairs and make a full rotation, the ...
Webp-adic monodromy theorem for de Rham representations and to give some background on p-adic representations. R´esum´e. — Cet article informel est une version longue de deux expos´es donn´es `a Padoue en Juin 2001 au “Trimestre Dwork”. Leur objet ´etait d’expliquer la d´emonstration du WebApr 12, 2024 · Since the trace of the matrix A in Eq.\eqref{EqFloquet.9} is zero, according to Liouville--Ostrogradski theorem, the Wronskian of two linearly independent solutions is 1. We immediately deduce that the determinant of any fundamental matrix is a constant. So the determinant of the monodromy matrix E is 1. Its eigenvalues are roots of the ...
WebAs an application, we prove, using the reduction modulo ptech- nique, that, for a smooth and proper DG algebra over a complex punctured disk, the monodromy of the Gauss-Manin connection on its periodic cyclic homology is quasi-unipotent. 1.1. Relative Fontaine-La … WebNov 18, 2010 · A Kohno–Drinfeld Theorem for the Monodromy of Cyclotomic KZ Connections. We compute explicitly the monodromy representations of “cyclotomic” analogs of the Knizhnik–Zamolodchikov differential system. These are representations of the type B braid group $$ {B_n^1}$$ . We show how the representations of the braid group …
WebMar 24, 2024 · Monodromy Theorem If a complex function is analytic in a disk contained in a simply connected domain and can be analytically continued along every polygonal arc in …
Webmonodromy datum (G,x) such that x = (ab2,b,ba−1),m = (2q,4,4), corresponding to the second Hur-witz equivalence class identified by Proposition 5.1. The following theorem identifies that H1(C,Q) has both a complex-valued piece and a symplectic piece. Theorem 5.8. Let C→ P1 be the G-Galois cover with local monodromy m = (2q,4,4) as ... lea county oil and gasWebFeb 10, 2024 · The action described in the above theorem is called the monodromy action and the corresponding homomorphism. ρ: π → Sym (F) is called the monodromy of p. Title: monodromy: Canonical name: Monodromy: Date of creation: 2013-03-22 13:26:20: Last modified on: 2013-03-22 13:26:20: Owner: mathcam (2727) Last modified by: lea county property lookupWebJun 6, 2024 · The idea of a monodromy transformation arose in the study of multi-valued functions (see Monodromy theorem). If $ S \rightarrow P ^ {1} ( \mathbf C ) $ is the Riemann surface of such a function, then by eliminating the singular points of the function from the Riemann sphere $ P ^ {1} ( \mathbf C ) $, an unbranched covering is obtained. The ... lea county personal injury lawyerlea county nm county clerk filing feesWebSep 2, 2024 · The monodromy theorem states that T k is quasi-unipotent, i.e., there are positive integers m k and d k such that. ( T k m k − I) d k = 0. Here, m k is the least … lea county probation officeWebThe p-adic local monodromy theorem In this chapter, we assert the p-adic local monodromy theorem, and sketch how it can be proved either using deep properties of p-adic differential equations, or using a theory of slope filtrations for Frobenius modules over the Robba ring. 1. Statement of the theorem Remark 18.1.1. lea county public records searchWebTHE MONODROMY-WEIGHT CONJECTURE DONU ARAPURA Deligne [D1] formulated his conjecture in 1970, simultaneously in the ‘-adic and Hodge theoretic settings. The Hodge … lea county nm jail