## Algebraic study of systems of partial differential equations, Issue 63 |

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### Contents

On the CauchyKovalevskaya theorem | 23 |

Algebraic aspects of Tx homology | 45 |

Index theorem in dimension 1 | 59 |

Copyright | |

1 other sections not shown

### Common terms and phrases

algebraic assume Cauchy problem Cauchy-Kovalevskaya theorem char(M characteristic variety codimension coefficients coherent Ox-module cokernel commutative diagram complex manifold consider cotangent Definition denote dim coker Pr dim ker être exact sequence filtered S-modules filtration Mk finite type Following Proposition following theorem free resolution functor grfc HELFFER Hence holonomic P-modules holonomic systems homomorphism hyperfunctions Index theorem induction hypothesis induction on q injective isomorphism Jk Mk JkMk Kashiwara Kashiwara's thesis Kawai ker Pr kernel l'Internet Let us set Math maximally overdetermined system Mémoires Mk-i Moreover morphism multiplicity neighborhood non-characteristic operator of degree Ox,x P-modules partial differential equations partial differential operators pseudo-differential operators quasi-free filtered regular filtration Sato Schapira sequence of coherent sheaf of rings sheaves SJÔSTRAND Spencer sequence Springer strict homomorphisms submanifold sufficient to prove supp(grM surjective system of linear systems of partial T>x-module theory torsion module torsion-free