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The monodromy theorem

Let F(x) denote the field of the rational functions in the variable x over the field F, which is the field of fractions of the polynomial ring F[x]. An element y = f(x) of F(x) determines a finite field extension [F(x) : F(y)]. This extension is generally not Galois but has Galois closure L(f). The associated Galois group of the extension [L(f) : F(y)] is called the monodromy group of f. WebThe rigid uniformization subsumes the monodromy operator. (As an aside, IMHO even for AV's admitting a principal polarization, it is a conceptual error to think about the …

Monodromy theorem - Encyclopedia of Mathematics

Webthe monodromy operator of an isolated hypersurface or complete intersection singularity. The investigation of this operator started in 1967 with the proof of the famous monodromy theorem (see §1). This theorem can be proved 1991 Mathematics Subject Classification. 14D05, 32S40 Key words. monodromy, zeta function, spectrum, isolated singularity WebThe construction essentially relies on properties of hypergeometric differential operators. For small m, we find billiard tables that generate these Teichmüller curves. We interpret some of the so-called Lyapunov exponents of the Kontsevich-Zorich cocycle as normalized degrees of a natural line bundle on a Teichmüller curve. lea county nm eagleweb https://magicomundo.net

Analytic continuation and two versions of Monodromy theorem

Web3.2 Path Lifting and the Monodromy Theorem Let p:X~ !Xbe a covering map over a topological space X. Let Zbe a topological space, and let f:Z!Xbe a continuous map from Zto X. A continuous map f~:Z!X~ is said to be a lift of the map f:Z!Xif and only if p f~= f. We shall prove various results concerning the existence and uniqueness of such lifts. WebErratum to "Nilpotent Connections and the Monodromy Theorem" pdf file(127 KB) (joint with Antonio Rojas-Leon and Pham Huu Tiep)Rigid Local Systems and Sporadic Simple Groups … WebMonodromy theorem ensures that there exists a holomorphic function extending G(z) = log(f(z)) in U. Picard’s little theorem Monodromy theorem is an important ingredient in … lea county nm county clerk records

arXiv:1507.00711v1 [math.AG] 2 Jul 2015

Category:From dynamics on surfaces to rational points on curves

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The monodromy theorem

Monodromy transformation - Encyclopedia of Mathematics

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