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15 July 2018 The p-curvature conjecture and monodromy around simple closed loops
Ananth N. Shankar
Duke Math. J. 167(10): 1951-1980 (15 July 2018). DOI: 10.1215/00127094-2018-0008

Abstract

The 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 has finite monodromy if its p-curvature vanishes modulo p, for almost all primes p. We prove that if the variety is a generic curve, then every simple closed loop on the curve has finite monodromy.

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Ananth N. Shankar. "The p-curvature conjecture and monodromy around simple closed loops." Duke Math. J. 167 (10) 1951 - 1980, 15 July 2018. https://doi.org/10.1215/00127094-2018-0008

Information

Received: 19 February 2017; Revised: 1 February 2018; Published: 15 July 2018
First available in Project Euclid: 26 June 2018

zbMATH: 06928114
MathSciNet: MR3827814
Digital Object Identifier: 10.1215/00127094-2018-0008

Subjects:
Primary: 11G30
Secondary: 14D06, 14G22

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 10 • 15 July 2018
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