The Grothendieck–Katz -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 -curvature vanishes modulo , for almost all primes . We prove that if the variety is a generic curve, then every simple closed loop on the curve has finite monodromy.
Duke Math. J.
167(10):
1951-1980
(15 July 2018).
DOI: 10.1215/00127094-2018-0008
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