We construct a logarithmic model of connections on smooth quasi-projective -dimensional geometrically irreducible varieties defined over an algebraically closed field of characteristic . It consists of a good compactification of the variety together with lattices on it which are stabilized by log differential operators, and compute algebraically de Rham cohomology. The construction is derived from the existence of good Deligne-Malgrange lattices, a theorem of Kedlaya and Mochizuki which consists first in eliminating the turning points. Moreover, we show that a logarithmic model obtained in this way, called a good model, yields a formula predicted by Michael Groechenig, computing the class of the characteristic variety of the underlying -module in the -theory group of the variety.
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Hélène Esnault, Claude Sabbah, Good Lattices of Algebraic Connections (with an Appendix by Claude Sabbah). Doc. Math. 24 (2019), pp. 271–301DOI 10.4171/DM/681