Good lattices of algebraic connections (with an appendix by claude sabbah)

We construct a logarithmic model of connections on smooth quasi-projective n-dimensional geometrically irreducible varieties defined over an algebraically closed field of characteristic 0. It consists of a good compactification of the variety together with (n+1) 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 D-module in the K-theory group of the variety.