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Journal Articles Documenta Mathematica Year : 2019

## Good lattices of algebraic connections

, (1)
1
Hélène Esnault
• Function : Author
Claude Sabbah

#### 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.

#### Domains

Mathematics [math] Algebraic Geometry [math.AG]

### Dates and versions

hal-02322150 , version 1 (21-10-2019)

### Identifiers

• HAL Id : hal-02322150 , version 1
• ARXIV :
• DOI :

### Cite

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

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