Geodesic
Good Lattices of Algebraic Connections (with an Appendix by Claude Sabbah)
Documenta mathematica, Tome 24 (2019), pp. 271-301
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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.
DOI : 10.4171/dm/681
Classification : 14F10, 14F40, 32C38
Mots-clés : de Rham cohomology, flat connection, good lattice, good model, characteristic variety 
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     author = {H\'el\`ene Esnault and Claude Sabbah},
     title = {Good {Lattices} of {Algebraic} {Connections} (with an {Appendix} by {Claude} {Sabbah)}},
     journal = {Documenta mathematica},
     pages = {271--301},
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Hélène Esnault; Claude Sabbah. Good Lattices of Algebraic Connections (with an Appendix by Claude Sabbah). Documenta mathematica, Tome 24 (2019), pp. 271-301. doi: 10.4171/dm/681

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