Grothendieck-katz p-curvature conjecture

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August undefined, 2024

WebGiven a linear differential equation with coefficients in $\mathbb{Q}(x)$, an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions is algebraic. After presenting motivating examples coming from various branches of mathematics, we advertise in an elementary way a beautiful … WebApr 11, 2024 · This approach has deep ramifications and leads to the still unsolved Grothendieck-Katz -curvature conjecture. Submission history From: Alin Bostan [ …

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WebJul 15, 2024 · Abstract. The Grothendieck–Katz p p -curvature conjecture is an analogue of the Hasse principle for differential equations. It states that a set of arithmetic … WebThe Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing p-curvatures for all but finitely many … gold price fluctuation

The p-curvature conjecture and monodromy around simple closed …

WebGrothendieck–Katz p-curvature conjecture. In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, … WebThe Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing p-curvatures for all but finitely many primes p, has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on P^1 − {0, 1, ∞}. We prove a variant of this ... WebGrothendieck–Katz p-curvature conjecture: differential equations: Alexander Grothendieck and Nick Katz: 98 Hadamard conjecture: combinatorics: Jacques Hadamard: 858 Herzog–Schönheim conjecture: group theory: Marcel Herzog and Jochanan Schönheim: 44 Hilbert–Smith conjecture: geometric topology: David Hilbert … headliner covina dj controller stand

On the Grothendieck conjecture on -curvatures for …

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WebNov 17, 2009 · Download a PDF of the paper titled Notes on the section conjecture of Grothendieck, by Feng-Wen An. Download PDF Abstract: In this short note, we will give … WebAug 1, 2024 · We prove the p-curvature conjecture for rank two vector bundles with connection on generic curves. Our ingredients include new deformation techniques for vector bundles with vanishing p-curvatures ... gold price expected in 2023WebAug 6, 2024 · 1. Introduction1.1.. This paper proves the Grothendieck–Katz p-curvature conjecture for rank two vector bundles with connection on generic curves.Formulated as follows, the conjecture gives an arithmetic criterion for certain differential equations on algebraic varieties to admit algebraic solutions. gold price for 2022

"WebGrothendieck’s p-curvature conjecture is a far reaching conjectural generalization of these ... [31] L. Di Vizio. Arithmetic theory of q-difference equations: the q-analogueof Grothendieck-Katz’s conjecture on p-curvatures. Invent. Math., 150(3), 2002. [32] T. Dreyfus, C. Hardouin, J. Roques, and M. F. Singer. On the nature of the generating " - Grothendieck-katz p-curvature conjecture

Grothendieck-katz p-curvature conjecture

WebThe Grothendieck–Katz p-curvature conjecture predicts that an arithmetic diﬀerential equation whose reduction modulo phas vanishing p- … WebThe Grothendieck–Katz p-curvature conjecture predicts that an arithmetic diﬀerential equation whose reduction modulo p has vanishing p-curvatures for all but ﬁnitely many primes p,hasﬁnite monodromy. It is known that it suﬃces to prove the conjecture for diﬀerential equations on P1− {0,1,∞}.

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WebThe Grothendieck-Katz p-curvature conjecture is an analogue of the Hasse Principle for diﬀerential equations. It states that a set of arithmetic diﬀerential equations on a variety … WebApr 11, 2024 · After presenting motivating examples coming from various branches of mathematics, we advertise in an elementary way a beautiful local-global arithmetic approach to these questions, initiated by Grothendieck in the late sixties. This approach has deep ramifications and leads to the still unsolved Grothendieck-Katz -curvature conjecture.

WebThe Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing p-curvatures for all but finitely many … 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 module with connection mod p underlies a { {\mathcal {D}}}_X -module structure.

WebJun 13, 2009 · In this paper, we prove certain cases of the well-known p -curvature conjecture of Grothendieck–Katz stated below. The conjecture posits that one can deduce algebraic solutions of certain differential equations when one has solutions after reducing modulo a prime for almost every prime.

WebThe result is motivated by the Grothendieck-Katz p -curvature conjecture, and gives a reformulation of the p -curvature conjecture in terms of isomonodromy. • Arithmetic representations of fundamental groups II: finiteness ( arXiv version, 2024, Duke Mathematics Journal version here) + Abstract

WebConjecture 1 (Grothendieck p-Curvature Conjecture). Suppose that for almost all maxi-mal ideals p of R, the p-curvature of (V/pV,∇) vanishes. Then the (complex) diﬀerential … headliner crystal sky petuniaWebConjecture 1.1 (Grothendieck-Katz p-curvature conjecture). Suppose that for almost all primes p, the p-curvature of (V/p,∇/p) vanishes. Then the diﬀerential equation (V,∇) has a full set of algebraic solutions, i.e. it becomes trivial on a ﬁnite etale cover of X. Katz in [6] proved that if the p-curvatures vanish for almost all p, then ... headliner czWebJun 13, 2009 · In this paper, we prove certain cases of the well-known p-curvature conjecture of Grothendieck–Katz stated below. The conjecture posits that one can … headliner cymbalsWebJul 15, 2024 · Abstract. The Grothendieck–Katz p p -curvature conjecture is an analogue of the Hasse principle for differential equations. It states that a set of arithmetic … headliner custom fabricWebWe use generalizations of the Borel–Dwork criterion to prove variants of the Grothedieck–Katz p-curvature conjecture and the conjecture of Ogus for some classes of abelian varieties over number fields. The Grothendieck–Katz ... Algorithms and Models for Genome Biology Zou, James Yang (2014-02-25) New advances in genomic … headliner danceWebJan 15, 2024 · In algebraic geometry, p-curvature is an invariant of a connection on a coherent sheaf for schemes of characteristic p > 0. It is a construction similar to a usual … gold price for coinsWebSee also[edit] Grothendieck–Katz p-curvature conjecture. Restricted Lie algebra. References[edit] Katz, N., "Nilpotent connections and the monodromy theorem", IHES … gold price for 1 oz