| Softcover ISBN: | 978-2-85629-909-8 |
| Product Code: | SMFMEM/163 |
| List Price: | $52.00 |
| AMS Member Price: | $41.60 |
| Softcover ISBN: | 978-2-85629-909-8 |
| Product Code: | SMFMEM/163 |
| List Price: | $52.00 |
| AMS Member Price: | $41.60 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 163; 2019; 138 ppMSC: Primary 14
Let \(\mathrm{W}\) be the ring of the Witt vectors of a perfect field of characteristic \(p\), \(\mathfrak{X}\) a smooth formal scheme over \(\mathrm{W}\), \(\mathfrak{X}^{\prime}\) the base change of \(\mathfrak{X}\) by the Frobenius morphism of \(\mathrm{W}\), \(\mathfrak{X}^{\prime}_{2}\) the reduction modulo \(p^{2}\) of \(\mathfrak{X}^{\prime}\) and \(X\) the special fiber of \(\mathfrak{X}\).
The author lifts the Cartier transform of Ogus-Vologodsky defined by \(\mathfrak{X}^{\prime}_{2}\) modulo \(p^{n}\). More precisely, the author constructs a functor from the category of \(p^{n}\)-torsion \(\mathscr{O}_{\mathfrak{X}^{\prime}}\)-modules with integrable \(p\)-connection to the category of \(p^{n}\)-torsion \(\mathscr{O}_{\mathfrak{X}}\)-modules with integrable connection, each subject to suitable nilpotence conditions. The author's construction is based on Oyama's reformulation of the Cartier transform of Ogus-Vologodsky in characteristic \(p\).
If there exists a lifting \(F:\mathfrak{X}\to \mathfrak{X}^{\prime}\) of the relative Frobenius morphism of \(X\), the author's functor is compatible with a functor constructed by Shiho from \(F\). As an application, the author gives a new interpretation of Faltings' relative Fontaine modules and of the computation of their cohomology.
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.
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Let \(\mathrm{W}\) be the ring of the Witt vectors of a perfect field of characteristic \(p\), \(\mathfrak{X}\) a smooth formal scheme over \(\mathrm{W}\), \(\mathfrak{X}^{\prime}\) the base change of \(\mathfrak{X}\) by the Frobenius morphism of \(\mathrm{W}\), \(\mathfrak{X}^{\prime}_{2}\) the reduction modulo \(p^{2}\) of \(\mathfrak{X}^{\prime}\) and \(X\) the special fiber of \(\mathfrak{X}\).
The author lifts the Cartier transform of Ogus-Vologodsky defined by \(\mathfrak{X}^{\prime}_{2}\) modulo \(p^{n}\). More precisely, the author constructs a functor from the category of \(p^{n}\)-torsion \(\mathscr{O}_{\mathfrak{X}^{\prime}}\)-modules with integrable \(p\)-connection to the category of \(p^{n}\)-torsion \(\mathscr{O}_{\mathfrak{X}}\)-modules with integrable connection, each subject to suitable nilpotence conditions. The author's construction is based on Oyama's reformulation of the Cartier transform of Ogus-Vologodsky in characteristic \(p\).
If there exists a lifting \(F:\mathfrak{X}\to \mathfrak{X}^{\prime}\) of the relative Frobenius morphism of \(X\), the author's functor is compatible with a functor constructed by Shiho from \(F\). As an application, the author gives a new interpretation of Faltings' relative Fontaine modules and of the computation of their cohomology.
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.
