Grothendieck monodromy

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August undefined, 2024

WebDec 18, 2024 · Monodromy is the name for the action of the homotopy groups of a space X X on fibers of covering spaces or locally constant ∞-stacks on X X. In point-set topology … WebI consider this latter proof to be part of Grothendieck's local monodromy theory, as one uses a similar method to prove the local monodromy theorem (at least, as …

Grothendieck connection - Wikipedia

WebTheorem 5.1 (Grothendieck’s l-adic monodromy theorem). Let Fbe an ‘-adic eld, where ‘6= pis prime. Let (ˆ;V) be a nite-dimensional representation of W Kover F. Then there exists a nite-index open subgroup HˆI Ksuch that ˆ(x) is unipotent for all x2H. Remark 5.2. A similar theorem is true if we replace W Kby G Kbecause unipo- Web5. Applications of the monodromy theorem The original area of application of the p-adic local monodromy theorem was in the subject of rigid cohomology; the name comes from the fact that it plays a role analogous to the ℓ-adic local monodromy theorem of Grothendieck in the subject of ´etale cohomology. In particular, shively police phone number

A $p$-adic local monodromy theorem Annals of Mathematics

WebOct 26, 2016 · Corollary (Grothendieck’s ‘-adic monodromy theorem). Let K be a local ﬁeld. Then any ‘-adic representation of GK coming from geometry is potentially semi … WebThe problem is that usually, in the books of algebraic geometry, quasi-unipotent monodromy is only discussed over a disc Δ ∗, i.e. for a 1-parameter family. In this case we know that for a fibration f: X → Δ, with monodromy representation ρ: π 1 ( Δ ∗) → A u t ( H i ( X 0)), the image ρ ( T) of a generator T of π 1 ( Δ ∗) is a ... WebAlexander Grothendieck1928- French Mathematician Alexander Grothendieck is regarded by many as one of the preeminent mathematicians of the twentieth century. He is … r.a. 11469

MONODROMY GROUPS OF INDECOMPOSABLE RATIONAL …

Grothendieck–Katz p-curvature conjecture - Wikipedia

WebIf K = C((t)), we can not apply Grothendieck’s theorem. But if the representation is the etale cohomology of some variety over K, then the eigenvalues of the monodromy action are roots of unity by the comparison theorem and the monodromy theorem for the singular cohomology. In this case, we can apply the bound using the Euler function. WebGrothendieck's solution is to consider the diagonal embedding The sheaf of ideals of in consists of functions on which vanish along the diagonal. Much of the infinitesimal … shively police reportsWebNov 5, 2016 · We investigate an analogue of the Grothendieck p-curvature conjecture, where the vanishing of the p-curvature is replaced by the stronger condition, that the module with connection mod p underlies a $${{\\mathcal {D}}}_X$$ D X -module structure. We show that this weaker conjecture holds in various situations, for example if the underlying … shively power and choice chapter summaries

"WebGeometric monodromy: the monodromy theorem for í Reduction of the purity theorem to the monodromy theorem Application of Rankin’s method Lecttt ure IV Proof of the … " - Grothendieck monodromy

Grothendieck monodromy

WebIn mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957 in order to develop the machinery of … Webtional function f(X) is its monodromy group, which is a set of permutations of nobjects. This monodromy group determines several properties of f(X). A fundamental problem is to classify all degree-nrational functions which have special behavior, meaning that their monodromy group Gis not one of the two \typical" groups, namely A n or S n. Many ...

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WebWEIGHT-MONODROMY CONJECTURE OVER EQUAL CHARACTERISTIC LOCAL FIELDS TETSUSHI ITO Abstract. The aim of this paper is to study certain properties of the weight ... By Grothendieck’s monodromy theorem ([ST], Appendix, see also [SGA7-I], I, Variante 1.3), there is an open subgroup J ⊂I WebIn mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as the polynomial case. It is a conjecture of Alexander Grothendieck from the late ...

Webﬁrst glance that Grothendieck called them dessins d’enfants (children’s drawings). We construct new invariants of the action of GQ on dessins d’enfants. In fact, ... are. Thus if I is a GQ-invariant of dessins (e.g. the monodromy group, the rational Nielsen class), so is I β. In [5], Ellenberg deﬁnes the class of Belyi- WebS/Gm,S] and monodromy invariant vanishing cycles 42 Appendix A. 47 References 50 Introduction The theory of vanishing cycles for the germ of an holomorphic function (Cn,0) →(C,0) was in-troduced by J. Milnor in his celebrated book [22]. The theory was developed in the algebraic setup by A. Grothendieck ([10]) and by P. Deligne ([11]).

WebAccording to Grothendieck monodromy theorem, l-adic galois representations of a local field corresponds to Weil-Deligne representations. However, given a galois representation, it is usually difficult to find the Weil-Deligne representations. (1) Is it possible to describe explicitly the Weil-Deligne representation associated to the Tate module ... WebNov 5, 2016 · We investigate an analogue of the Grothendieck p-curvature conjecture, where the vanishing of the p-curvature is replaced by the stronger condition, that the …

WebIn mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose …

WebJan 14, 2015 · Grothendieck was born in Berlin in 1928 to a Russian Jewish father and a German Protestant mother. After being separated from his parents at the age of five, he … shively police scannerWebJul 25, 2024 · I'm trying to understand variations of Hodge structure. I understand that this is a very broad field, and that many of the concepts have been extended to algebraic geometry over fields other than $\mathbb{C}$, and so forth.In particular, there is a version of the monodromy theorem by Grothendieck, which is rather incomprehensible to me. shively pronunciationWebGrothendieck conjectured that there should be a p-adic version of Hodge theory that is, a method for comparing cohomologies of varieties over the p-adic numbers. In particular, he envisioned that such a theory would provide ... pondering the weight monodromy conjecture that set Scholze on the path to de ning the concept of perfectoid spaces ... r.a 11362http://personal.psu.edu/mup17/Research/CM605.pdf ra 11494 bayanihan to recover as one act pdfWebGrothendieck’s ‘-adic monodromy theorem implies that these are in bijection with certain Weil-Deligne representations, which are pairs (r;N) of a continuous (here this means … shively post officeWebGrothendieck monodromy theorem for l-adic sheaves. Suppose that F is a local field, G F its Galois group, I the inertia subgroup, k its residue field. Let X be a finite type scheme … shively power and choiceWebDedicated to Ludwig Dmitrievich Faddeev on the occasion of his 70th birthday Abstract. Grothendieck's dessins d'enfants are applied to the theory of the sixth Painleve and Gauss hypergeometric functions, two classical special functions of iso- monodromy type. It is shown that higher-order transformations and the Schwarz table for the Gauss … shively post office phone number