ON THE p−CURVATURES OF t-CONNECTIONS OVER A RELATIVE SMOOTH PROJECTIVE SCHEME
DOI:
https://doi.org/10.56764/hpu2.jos.2022.2.1.102-111- Keywords:
- t-bundles
- p-curvature
- Hitchin morphism
Abstract
Let be a global function of an integral -scheme and be a smooth projective scheme over . We show that the characteristic polynomial of the curvature of an integrable connection over is horizontal.
References
B. Dwork, Lectures on p-adic differential equations, volume 253 of Grundlehren der mathematischen Wissenschaften. Springer, New York, 1982.
H. Esnault, M. Groechenig, Rigid connections and F-isocrytals, Acta Mathematica, Volume 225 (2020), Number 1, p. 103 – 158.
N. Hitchin, Stable bundles and intergrable systems, Duke Mathematical Journal 54 (1987), pp. 91-114.
T. Honda, Algebraic differential equations, In Symposia Mathematica, Vol. XXIV, pages 169–204. Academic Press, London, 1981.
N.M. Katz, Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Publications math'ematiques de I.H.'E.S. 39 (1970), pp. 175-232.
Y. Laszlo and C. Pauly, On the Hitchin morphism in positive characteristic, Internat. Math. Res. Notices (2001), no. 3, pp. 129-143.
T. Mochizuki, Good formal structure for meromorphic flat connections on smooth projective surfaces, Advanced Studies Pure Mathematics 54 (2009), Algebraic Analysis and Around, pp.223–253.
Carlos T.Simpson, Moduli of representations of the fundamental group of a smooth projective variety II, Publications math'ematiques de I.H.'E.S. 80 (1994), pp.5-79.
