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.
"The -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