Esnault, Hélène; Sabbah, Claude

Good Lattices of Algebraic Connections (with an Appendix by Claude Sabbah)

Doc. Math. 24, 271-301 (2019)
DOI: 10.25537/dm.2019v24.271-301
Communicated by Takeshi Saito


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 \(\mathcal{D}\)-module in the \(K\)-theory group of the variety.

Mathematics Subject Classification

14F40, 14F10, 32C38


flat connection, good lattice, good model, de Rham cohomology, characteristic variety


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Esnault, Hélène
Freie Universität Berlin, Mathematik, Arnimallee 3, 14195 Berlin, Germany
Sabbah, Claude
CMLS, École Polytechnique, CNRS, Université Paris-Saclay, F-91128 Palaiseau cedex, France