## De Rham cohomology of differential modules on algebraic varieties"â€¦A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrongâ€¦This is a nicely-written book [that] studies algebraic differential modules in several variables."--Mathematical Reviews |

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### Contents

Regularity in several variables | 1 |

4 Comparison theorem for algebraic vs rigidanalytic | 4 |

Irregularity in several variables | 49 |

Copyright | |

7 other sections not shown

### Common terms and phrases

adapted basis affine neighborhood affine open assume base change bicomplex closed immersion closed point codimension coherent extension coherent sheaf coordinatized elementary fibration Corollary cyclic vector decomposition defined Definition denote devissage diagram diff.op differential module differential operator direct image divisor divisorial valuation divisorially valued function dual etale covering etale locally etale morphism etale neighborhood etale topology exact sequence exists exponents fiber finite etale finite rank follows formal function field functor Gauss-Manin connection hence indicial polynomial induces integrable connection integral curves inverse image isomorphism Lemma locally free log dominant log schemes MIC(X morphism of models morphism of smooth natural morphism Newton polygon open subset Poincare-Katz rank point Q projective Proof Proposition rational elementary fibration regular connection Remark replace resp Rham cohomology Rham complex sheaf with integrable smooth connected smooth morphism spectral sequence surjective trivial tubular neighborhood valued function field Vx/s Zariski