## 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 |

1 Geometric models of divisorially valued function fields | 2 |

4 Comparison theorem for algebraic vs rigidanalytic | 4 |

Copyright | |

33 other sections not shown

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### Common terms and phrases

assume base change bicomplex closed immersion closed point codimension coefficients Coh(X coherent sheaf comparison theorem coordinatized elementary fibration Corollary cyclic vector decomposition defined definition denote devissage diagram Diff diff.op differential module differential operator direct image divisor divisorially valued function dual etale covering etale locally etale morphism etale neighborhood etale topology exact sequence exists exponents fiber finite rank flat follows formal function field functor Gauss-Manin connection hence indicial polynomial induces integrable connection inverse image isomorphism Lemma Let f locally free log dominant log schemes MIC(X morphism of models morphism of smooth Newton polygon open subset p-adic Poincare-Katz rank point Q projective Proof Proposition pv(M rational elementary fibration regular connection relative dimension Remark replace resp Rham cohomology Rham complex RlDRf sheaf with integrable singular smooth connected smooth morphism spectral sequence surjective trivial tubular neighborhood valuation valued function field Vx/s Zariski