For example, the theory of covering spaces was invented to clarify the concept of an algebraic function and its polydromy. On a monodromy theorem for sheaves of local fields and. A potential problem of this analytic continuation along a. Monodromy and differential equations a related context in which monodromy groups arise is that of differential equations. Monodromy groups of indecomposable rational functions \random degreen rational function should have monodromy group a n or s n. Some older work can be found here listed alphabetically by title recent work is below most recent first.
Kedlaya submitted on 11 oct 2001, last revised 1 jan 2003 this version. We shall develop the results of this chapter in the context of manifolds definition 1 in 2. The monodromy group of an algebraic function wolfram. This gives an elementary counter example to the converse of. This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a padic rigid analytic. Schwarz reflection principle, analytic continuation along a path, monodromy theorem. A potential problem of this analytic continuation along a curve strategy is there are usually many. Monodromy and asymptotic properties of certain multiple. 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 rational homological monodromy of a complex hypersurface singularity is strongly invertible. The riemann zeta function and the prime numbers theorem 97 10. In particular, in the case of admissible regular sheaves of local fields.
Around 1990, kohno ko and drinfeld d2 proved a rather astonishing result, now known as the kohnodrinfeld theorem. Sc hub youtube channel me aapka sawagt hai, hamara m. Topic cover state proof explained lebesgue dominated convergence theorem pdf file download by. Real and imaginary parts of an analytic function satisfy laplace equation. The monodromy theorem for compact k\ahler manifolds and smooth quasiprojective varieties by nero budur, yongqiang liu and botong wang download pdf 224 kb. Weildeligne representations and padic hodge theory. Proof of the first homotopy version of the monodromy theorem by iit madras. A adic local monodromy theorem annals of mathematics. In complex analysis, the monodromy theorem is an important result about analytic continuation of a complexanalytic function to a larger set.
Download book pdf complex analysis in one variable pp 5368 cite as. Laurent series, casoratiweierstrass theorem, poles, residues, residue theorem and its applications to contour integrals, meromorphic functions, argument principle, rouches theorem. Work of many mathematicians ritt, zariski, guralnick, thompson, aschbacher. Homotopy continuation has become a standard technique to find approximations of solutions of polynomial systems. Proof of the first homotopy version of the monodromy theorem. Today, i read about monodromy, and the monodromy representation of. We study the topology of the punctured disc defined over a nonarchimedean field of characteristic zero. We give an analytic greeneliouville theorem, an entire free plurisubharmonic function is a sum of hereditary and. General method for building the riemann surface of a. A nogo theorem for monodromy inflation view the table. Im right now learning about monodromy from selfstudying rick mirandas fantastic book algebraic curves and riemann surfaces.
Let f,d be a function element which admits unrestricted. There is an early popular text on the subject and its applications in. The fact stated below is not required for our proof of theorem 8. 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. On a monodromy theorem for sheaves of local fields and applications. Theorem if n 2d, then the monodromy group is indeed arithmetic. He is best known for work on the weil conjectures, leading to a complete proof in 1973. The definition of analytic continuation along a curve is a bit technical, but the basic idea is. The monodromy theorem for compact k\ahler manifolds and. Monodromy groups of indecomposable rational functions. Department of mathematics, boston university, 111 cummington street, 02215, boston, ma, usa. Among the many papers written on ahypergeometric equations there are very few papers dealing with the monodromy group of these.
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. Therefore scherks theorem implies the monodromy theorem. Local monodromy in nonarchimedean analytic geometry. For example, if one starts at a point a, 0 \displaystyle a,0 a, 0. We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation. Noncommutative free universal monodromy, pluriharmonic. We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. 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. In complex analysis, the monodromy theorem is an important result about analytic continuation. For a nitedimensional gmodule v, r c is the following connection on the trivial vector bundle h reg v. Analytic continuation along arcs and the monodromy theorem.
On monodromy representation of period integrals associated. As the name implies, the fundamental meaning of monodromy. The idea is that one can extend a complexanalytic function. Solving polynomial systems via homotopy continuation and. Monodromy of boussinesq elliptic operators springerlink. We shall prove various results concerning the existence and uniqueness of such lifts. We strengthen these results in our main theorem as follows. Extending holomorphic motions and monodromy 55 theorem 2. Pdf on a monodromy theorem for sheaves of local fields and. The theorem states that quantum groups can be used to describe the monodromy. We discuss the history of the monodromy theorem, starting from weierstra. We will now show that the discrete and continuous variants of analytic continuation. 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.
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. Its global objects are classified by their monodromy, a functor from the poincare groupoid of x to c. A general stratification theorem for exponential sums, and applications pdf. Cb be a holomorphic motion where v is a connectedcomplexmanifoldwithabasepoint.
721 689 1452 629 658 888 183 1043 645 819 1046 1048 440 1294 952 104 109 1031 252 481 809 937 1234 342 1529 503 1001 49 174 524 562 1271 1128 1344 978 229 570 642 426 880 1497 1390