Monodromy theorem proof pdf

Proof of the divergence theorem let f be a smooth vector eld dened on a solid region v with boundary surface aoriented outward. X be a continuous map, and let wbe a point of x satisfying pw h0. The postcritical set is the union of six lines, and. This cover can be visualized as the helicoid as defined in the helicoid article restricted to.

The hodge theoretic statement, amounted to the existence of what is now called a limit mixed hodge structure. Let f,d be a function element and let g be a region containing d such that f,d admits unrestricted continuation in g. We also remark that the present theorem 3 is an improvement of theorem 1 of the authors paper 4. The third proof was inspired by hidas work on padic monodromy in 14 see also 16 and drew on an argument in 4. The theorem below provides certain evidence toward our expected hodge isomorphism.

Deligne in the course of the proof of the weil conjecture in 1. If a complex function is analytic at a point of a bounded simply connected domain and can be continued analytically along every curve from the point, then. This is done to keep the statements relatively simple, and manifolds are ample for the applications we have in mind. The topological proof of abelruffini theorem henryk zoladek abstract. D, can be analytically continued along any path in d, then the branch of an analytic function fz. The proof of this theorem is inspired by drinfelds proof of the kohnodrinfeld theorem d2. Annals of mathematics, 160 2004, 93184 a padic local monodromy theorem by kiran s.

Analytic continuation and two versions of monodromy theorem. Venkata balaji,department of mathematics,iit madras. Before stating and proving the monodromy theorem, we need two lemmas and a definition. Since a plane curve singularity is reducible if and only if hc. Covering maps and the monodromy theorem tcd maths home. A simple proof of the geometric fractional monodromy theorem. We strengthen these results in our main theorem as follows. Mod07 lec28 proof of the first homotopy version of the. Proof of theor em 2 by applying integrable surgery, we can assume that the bifurcation. Covering spaces and the monodromy theorem springerlink.

We define ht s, l as the vector space of forms of the first kind in fp,jatl, and h s, l as the complex conjugate of hi s,l. A nogo theorem for monodromy inflation article pdf available in journal of cosmology and astroparticle physics 201603 october 2015 with 9 reads how we measure reads. As you might know, analytic continuation works as follows. It is shown that the monodromy of the casimir connection and the. Ma525 on cauchys theorem and greens theorem 3 the proof for this theorem will be presented in section 8. Pdf we prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. A adic local monodromy theorem annals of mathematics. Monodromy theorem article about monodromy theorem by the. We also get lifts with q, rather than q, coe cients, in contrast to theorem. If k is a global eld, then every abelian variety ak of hall type has big monodromy. The pentagram map commutes with projective transformations and therefore must 3. Ok so we have this rectangle which is product of the closed interval a. For example, if one starts at a point a, 0 \ displaystyle a,0 a, 0.

The fractional monodromy of a liouville integrable hamiltonian system over a loop. The monodromy theorem gives conditions under which the analytic continuations are path independent. The padic local monodromy theorem in this chapter, we assert the padic local monodromy theorem, and sketch how it can be proved either using deep properties of padic di. The monodromy theorem in as important theorem in the field of complex analysis. We link condition 1 in the case n 2 to the niteness of a certain subgroup of the unitary group of an explicit skewhermitian form implicitly, this is the monodromy group of the gauss hypergeometric function, but we do not use this. We prove monodromy theorem for local vector fields be. Using this, we complete the proof that all semistable elliptic curves are. The proof uses arithmetic geometry, especially the weight spectral sequence. Perfectoid spaces and the weightmonodromy conjecture. Suppose that fz is a real function of complex variable whose derivative exists at. Scholze introduced a new method in 7 to study the weight monodromy conjecture and proved it for smooth complete intersections in smooth toric varieties, stated later as theorem 6. This was solved by schmid s a couple of years later. The case for small n, either even or odd, is similar to the case for large n, but the argument is somewhat less transparent.

Monodromy of elliptic surfaces fedor bogomolov and yuri tschinkel january 25, 2006 1 introduction let e b be a nonisotrivial jacobian elliptic. Pdf on a monodromy theorem for sheaves of local fields and. Modular elliptic curves and fermats last theorem by andrewjohnwiles fornada,claire,kateandolivia. Finally i wish to thank trfing and bjsrk for interesting discussions on the subject. In general, if is a simplyconnected region and is an analytic function on disc such that the germ at of admits an analytic continuation along any curve in from to. Finally, one proves the uniqueness of quasicoxeter quasitrian. We compute the iterated monodromy group for a postcritically. Big monodromy theorem for abelian varieties over nitely. The method is restrictive in the sense that any further extension would seem to be relied on the monodromy weight conjecture in the mixed characteristic case, among other di. Monodromy and asymptotic properties of certain multiple. Proof of the first homotopy version of the monodromy theorem lecture 30.

In complex analysis, the monodromy theorem is an important result about analytic continuation of a complexanalytic function to a larger set. Furthermore, hall has proved recently 12 the following theorem which in our notation reads. Existence and uniqueness of analytic continuations on nearby paths lecture 28. This proof relies on the nonsolvability of the monodromy group of a general algebraic function. A simple proof of the geometric fractional monodromy theorem broerefstathioulukina 2010 is presented. The monodromy theorem for compact k ahler manifolds and smooth quasiprojective varieties yongqiang ted liu joint work with nero budur and botong wang ku leuven geometry, algebra and combinatorics of moduli spaces and con gurations dobbiaco, february 22 2017 yongqiang liu ku leuven the monodromy theorem dobbiaco, february 22 2017 1 17. The monodromyweight conjecture donu arapura deligne d1 formulated his conjecture in 1970, simultaneously in the adic and hodge theoretic settings. A sufficient criterion for the singlevaluedness of a branch of an analytic function. Okay so we continue with the proof of the monodromy theorem. In complex analysis, the monodromy theorem is an important result about analytic continuation. Sketches of the ideas of the proofs can be found at the beginning of these sections. Is the monodromy action of the universal covering of a riemann surface faithful.

M proof of the divergence theorem and stokes theorem in this section we give proofs of the divergence theorem and stokes theorem using the denitions in cartesian coordinates. In this case the monodromy group is infinite cyclic and the covering space is the universal cover of the punctured complex plane. Next we will derive several applications of the monodromy theorem. We present a proof of the nonsolvability in radicals of a general algebraic equation of degree greater than four. Monodromy is the study of how objects \run round a singularity, and so the viewpoint of this paper shall be geometric. It can be viewed as the space of antiholomorphic lvalued forms, whose complex conjugate is of the first kind. Iterated monodromy for a twodimensional map james belk and sarah koch abstract. We also discuss the very recent results of litt which in particular imply a suitable analog for the etale fundamental group. Monodromy conjecture and proof of veys conjecture marco daddezio february 28, 2017 notation today fwill be a number. Monodromy theorems in the affine setting 15 is controlled by a bicomplex, namely the dynkinhochschild bicomplex. Let d be a simplyconnected domain in the complex space cn, n.