with the collaboration of Jeng-Daw Yu
| Softcover ISBN: | 978-2-85629-887-9 |
| Product Code: | SMFMEM/156 |
| List Price: | $60.00 |
| AMS Member Price: | $48.00 |
with the collaboration of Jeng-Daw Yu
| Softcover ISBN: | 978-2-85629-887-9 |
| Product Code: | SMFMEM/156 |
| List Price: | $60.00 |
| AMS Member Price: | $48.00 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 156; 2018; 126 ppMSC: Primary 14; 32
The author introduces the category of irregular mixed Hodge modules consisting of possibly irregular holonomic \(D\)-modules which can be endowed in a canonical way with a filtration known as the irregular Hodge filtration. Mixed Hodge modules with their Hodge filtration naturally belong to this category, as well as their twist by the exponential of any meromorphic function. This category is stable by various standard functors, which produce many more filtered objects.
The irregular Hodge filtration satisfies the \(E_1\)-degeneration property with respect to any projective morphism. This generalizes some results previously obtained by H. Esnault, J.-D.Yu, and the author. The author also shows that, modulo a condition on eigenvalues of monodromies, any rigid irreducible holonomic \(D\)-module on the complex projective line underlies an irregular pure Hodge module. In a chapter written jointly with Jeng-Daw Yu, the author makes explicit the case of irregular mixed Hodge structures for which the author proves a Thom-Sebastiani formula.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians interested in mixed Hodge modules.
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The author introduces the category of irregular mixed Hodge modules consisting of possibly irregular holonomic \(D\)-modules which can be endowed in a canonical way with a filtration known as the irregular Hodge filtration. Mixed Hodge modules with their Hodge filtration naturally belong to this category, as well as their twist by the exponential of any meromorphic function. This category is stable by various standard functors, which produce many more filtered objects.
The irregular Hodge filtration satisfies the \(E_1\)-degeneration property with respect to any projective morphism. This generalizes some results previously obtained by H. Esnault, J.-D.Yu, and the author. The author also shows that, modulo a condition on eigenvalues of monodromies, any rigid irreducible holonomic \(D\)-module on the complex projective line underlies an irregular pure Hodge module. In a chapter written jointly with Jeng-Daw Yu, the author makes explicit the case of irregular mixed Hodge structures for which the author proves a Thom-Sebastiani formula.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in mixed Hodge modules.
