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arXiv · 0706.0671

Sur la p-dimension des corps

Ofer Gabber·Fabrice Orgogozo
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Abstract

Let A be an excellent integral henselian local noetherian ring, k its residue field of characteristic p>0 and K its fraction field. Using an algebraization technique introduced by the first named author, and the one-dimension case already proved by Kazuya KATO, we prove the following formula: cd_p(K) = dim(A) + p-rank(k), if k is separably closed and K of characteristic zero. A similar statement is valid without those assumptions on k and K.

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Ofer Gabber, Fabrice Orgogozo. 2007-06-05. Sur la p-dimension des corps. https://doi.org/10.1007/s00222-008-0133-y

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