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arXiv · 1812.06278

Good lattices of algebraic connections

Hélène Esnault·Claude Sabbah
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Abstract

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.

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Hélène Esnault, Claude Sabbah. 2019-03-31. Good lattices of algebraic connections. https://doi.org/10.25537/dm.2019v24.271-301

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