Grothendieck-katz p-curvature conjecture
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
Grothendieck-katz p-curvature conjecture
Did you know?
WebThe Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo phas vanishing p- … WebThis allows us to prove new cases of the Grothendieck–Katz $p$-curvature conjecture. We also prove the existence of a complete companion correspondence for $F$-isocrystals stemming from irreducible cohomologically rigid connections. Funding Statement
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. 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 …
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 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 …
WebAug 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.
WebJul 27, 2024 · The conjecture for rank one case follows from the solution of Grothendieck--Katz p-curvature conjecture, and for some versions of rigid cases should follow from Katz's work on rigid local systems. The conjecture implies that in a spread-out of any complex elliptic curve, there will be infinitely many supersingular primes, a result of N. … elements creative nonfictionWebJan 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 … football teams in perth scotlandWebGrothendieck’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 elements crossword puzzle answerWebThe 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 ... football teams in poznanWebThe p-adic Mehta Integral Abstract : The Mehta integral is the canonical partition function for 1-dimensional log-Coulomb gas in a harmonic potential well. Mehta and Dyson showed that it also determines the joint probability densities for the eigenvalues of Gaussian random matrix ensembles, and Bombieri later found its explicit form. football teams in peterboroughWebGiven 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 … football teams in north carolinaWebIn 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 1960s, and … football teams in norwich looking for players