An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors

Amit Hogadi; Supriya Pisolkar

Acta Arithmetica, Tome 161 (2013), p. 165-171 / Harvested from The Polish Digital Mathematics Library

Résumé

Let L/K be a finite Galois extension of complete discrete valued fields of characteristic p. Assume that the induced residue field extension $k_{L} / k_{K}$ is separable. For an integer n ≥ 0, let $W_{n} (_{L})$ denote the ring of Witt vectors of length n with coefficients in $_{L}$ . We show that the proabelian group ${H^{1} (G, W_{n} (_{L}))}_{n \in ℕ}$ is zero. This is an equicharacteristic analogue of Hesselholt’s conjecture, which was proved before when the discrete valued fields are of mixed characteristic.

Publié le : 2013-01-01

Zbl 1280.11077

EUDML-ID : urn:eudml:doc:278878

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     author = {Amit Hogadi and Supriya Pisolkar},
     title = {An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors},
     journal = {Acta Arithmetica},
     volume = {161},
     year = {2013},
     pages = {165-171},
     zbl = {1280.11077},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-2-4}
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Amit Hogadi; Supriya Pisolkar. An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors. Acta Arithmetica, Tome 161 (2013) pp. 165-171. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-2-4/