科研之友
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摘要
In a previous paper, we stated a general almost purity theorem in the style of Faltings: if R is a ring for which the Frobenius maps on finite p-typical Witt vectors over R are surjective, then the integral closure of R in a finite etale extension of R[p(-1)] is "almost" finite kale over R. Here, we use almost purity to lift the finite etale extension of R[p(-1)] to a finite etale extension of rings of overconvergent Witt vectors. The point is that no hypothesis of p-adic completeness is needed; this result thus points towards potential global analogues of p-adic Hodge theory. As an illustration, we construct (phi, Gamma)-modules associated with Artin Motives over Q. The (phi, Gamma)-modules we construct are defined over a base ring which seems well-suited to generalization to a more global setting; we plan to pursue such generalizations in later work.
- 出版日期2015-1-15
