Purely inseparable extensions and ramification filtrations
In this article, the authors investigate the shift of Abbes and Saito's ramification filtrations of the absolute Galois group of a complete discrete valuation field of positive characteristic under a purely inseparable extension. They also study a functoriality property for characteristic forms. This article has two parts. The first part is sections 2--4. After preliminaries on fields, the authors review Abbes and Saito's ramification filtrations in section 3 and they prove a related Theorem section 4. The second part is sections 5--7. The authors introduce the geometric notation in section 5. In section 6, they recall the geometric ramification and characteristic forms for etale covers and prove the functoriality of characteristic forms. At last, they apply a functoriality property to fields.
Abbes and Saito's ramification filtration
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