https://hal-polytechnique.archives-ouvertes.fr/hal-02322150Esnault, HélèneHélèneEsnaultSabbah, ClaudeClaudeSabbahCMLS - Centre de Mathématiques Laurent Schwartz - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueGood lattices of algebraic connectionsHAL CCSD2019[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Sabbah, Claude2019-10-21 15:36:122020-07-07 17:22:042019-10-21 15:36:12enJournal articles10.25537/dm.2019v24.271-3011We 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.