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Good lattices of algebraic connections

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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https://hal-polytechnique.archives-ouvertes.fr/hal-02322150
Contributor : Claude Sabbah <>
Submitted on : Monday, October 21, 2019 - 3:36:12 PM
Last modification on : Tuesday, July 7, 2020 - 5:22:04 PM

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Hélène Esnault, Claude Sabbah. Good lattices of algebraic connections. Documenta Mathematica, Universität Bielefeld, 2019, ⟨10.25537/dm.2019v24.271-301⟩. ⟨hal-02322150⟩

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