Kedlaya submitted on 11 oct 2001, last revised 1 jan 2003 this version. Some older work can be found here listed alphabetically by title recent work is below most recent first. Laurent series, casoratiweierstrass theorem, poles, residues, residue theorem and its applications to contour integrals, meromorphic functions, argument principle, rouches theorem. Schwarz reflection principle, analytic continuation along a path, monodromy theorem. A potential problem of this analytic continuation along a. Noncommutative free universal monodromy, pluriharmonic. Analytic continuation along arcs and the monodromy theorem. We give an analytic greeneliouville theorem, an entire free plurisubharmonic function is a sum of hereditary and.
Around 1990, kohno ko and drinfeld d2 proved a rather astonishing result, now known as the kohnodrinfeld theorem. We strengthen these results in our main theorem as follows. Sc hub youtube channel me aapka sawagt hai, hamara m. Weildeligne representations and padic hodge theory. We will now show that the discrete and continuous variants of analytic continuation. Monodromy groups and linearly polymorphic functions. Venkataramana tifr monodromy and arithmetic groups february 10, 2015 7 30. A adic local monodromy theorem annals of mathematics. Pdf twisted monodromy homomorphisms and massey products. As the name implies, the fundamental meaning of monodromy. The idea is that one can extend a complexanalytic function. On a monodromy theorem for sheaves of local fields and.
In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they run round a singularity. We study the topology of the punctured disc defined over a nonarchimedean field of characteristic zero. Im right now learning about monodromy from selfstudying rick mirandas fantastic book algebraic curves and riemann surfaces. Today, i read about monodromy, and the monodromy representation of. For a nitedimensional gmodule v, r c is the following connection on the trivial vector bundle h reg v. He is best known for work on the weil conjectures, leading to a complete proof in 1973. On a monodromy theorem for sheaves of local fields and applications. Monodromy and asymptotic properties of certain multiple. Monodromy is the study of how objects \run round a singularity, and so the viewpoint of this paper shall be geometric. There is an early popular text on the subject and its applications in.
Download book pdf complex analysis in one variable pp 5368 cite as. A potential problem of this analytic continuation along a curve strategy is there are usually many. Covering spaces and the monodromy theorem springerlink. Theorem if n 2d, then the monodromy group is indeed arithmetic. Monodromy groups of indecomposable rational functions. Proof of the first homotopy version of the monodromy theorem by iit madras.
The monodromy group of an algebraic function wolfram. We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. This demonstration shows the structure of the branches of a multivalued function defined by a polynomial equation, illustrating the transitions between the branches along paths going around a. Cb be a holomorphic motion where v is a connectedcomplexmanifoldwithabasepoint. The theorem states that quantum groups can be used to describe the monodromy. We shall prove various results concerning the existence and uniqueness of such lifts. The monodromy theorem for compact k\ahler manifolds and smooth quasiprojective varieties by nero budur, yongqiang liu and botong wang download pdf 224 kb. The definition of analytic continuation along a curve is a bit technical, but the basic idea is. Solving polynomial systems via homotopy continuation and. The riemann zeta function and the prime numbers theorem 97 10. Local monodromy in nonarchimedean analytic geometry. We calculate two differenent monodromy representations of period integrals for the affine variety x 2,2 obtained by the dual polyhedron mirror variety construction from y. Extending holomorphic motions and monodromy 55 theorem 2. Work of many mathematicians ritt, zariski, guralnick, thompson, aschbacher.
Topic cover state proof explained lebesgue dominated convergence theorem pdf file download by. We discuss the history of the monodromy theorem, starting from weierstra. This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a padic rigid analytic. Its global objects are classified by their monodromy, a functor from the poincare groupoid of x to c. Among the many papers written on ahypergeometric equations there are very few papers dealing with the monodromy group of these.
The fact stated below is not required for our proof of theorem 8. Therefore scherks theorem implies the monodromy theorem. Monodromy of boussinesq elliptic operators springerlink. Monodromy groups of indecomposable rational functions \random degreen rational function should have monodromy group a n or s n. The rational homological monodromy of a complex hypersurface singularity is strongly invertible. We shall develop the results of this chapter in the context of manifolds definition 1 in 2. In complex analysis, the monodromy theorem is an important result about analytic continuation. A nogo theorem for monodromy inflation view the table. For example, if one starts at a point a, 0 \displaystyle a,0 a, 0.
In this paper we recall these notions from the point of view of higher category theory and then define the 2 monodromy of a locally constant stack with values in a 2category as a 2functor from the homotopy 2groupoid into the 2category. Department of mathematics, boston university, 111 cummington street, 02215, boston, ma, usa. The following is a simpler version concerning the uniqueness of the monodromy theorem. Monodromy theorems in the affine setting where f g. In particular, in the case of admissible regular sheaves of local fields. We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation. In complex analysis, the monodromy theorem is an important result about analytic continuation of a complexanalytic function to a larger set. Monodromy is the study of how objects \run round a singularity, and so the viewpoint of this paper shall be. Note on the deck transformations group and the monodromy group zoladek, henryk, topological methods in nonlinear analysis, 2002 on non fundamental group equivalent surfaces teicher, mina and.
Let f,d be a function element which admits unrestricted. Proof of the first homotopy version of the monodromy theorem. Monodromy and differential equations a related context in which monodromy groups arise is that of differential equations. Homotopy continuation has become a standard technique to find approximations of solutions of polynomial systems. We establish a generalization of the padic local monodromy theorem of andre, mebkhout, and the author in which differential equations on rigid analytic. For example, the theory of covering spaces was invented to clarify the concept of an algebraic function and its polydromy. The idea is that one can extend a complexanalytic function from here on called simply analytic function along curves starting in the original domain of the function and ending in the larger set. The first method that gives a full representation of the fundamental group of the complement to singular loci relies on the generalised picardlefschetz theorem.
A general stratification theorem for exponential sums, and applications pdf. The monodromy theorem for compact k\ahler manifolds and. General method for building the riemann surface of a. Real and imaginary parts of an analytic function satisfy laplace equation. On monodromy representation of period integrals associated.
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