On the cohomology of Witt vectors of p-adic integers and a conjecture of Hesselholt

JOURNAL OF NUMBER THEORY

卷:131

Article

Hogadi, Amit¹  Pisolkar, Supriya¹ 

[1] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India

关键词: Galois cohomology;    Witt vectors;    p-Adic fields;    Hesselholt's conjecture;   

DOI  :  10.1016/j.jnt.2011.03.004

来源: Elsevier

【 摘 要 】

Let K be a complete discrete valued field of characteristic zero with residue field k(K) of characteristic p > 0. Let L/K be a finite Galois extension with Galois group G such that the induced extension of residue fields k(L)/k(K) is separable. Hesselholt (2004) [2] conjectured that the pro-abelian group {H(1)(G, W(n)(O(L)))}(n is an element of N) is zero, where O(L). is the ring of integers of L and W(O(L)) is the ring of Witt vectors in O(L) w.r.t. the prime p. He partially proved this conjecture for a large class of extensions. In this paper, we prove Hesselholt's conjecture for all Galois extensions. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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