TY - JOUR

T1 - A simplified proof of Hesselholt's conjecture on Galois cohomology of Witt vectors of algebraic integers

AU - Ong, Wilson

PY - 2012/12

Y1 - 2012/12

N2 - Let K be a complete discrete valuation 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 = Gal(L=K) and suppose that the induced extension of residue fields k L=k K is separable. Let W n ( ) denote the ring of p-typical Witt vectors of length n. Hesselholt ['Galois cohomology of Witt vectors of algebraic integers', Math. Proc. Cambridge Philos. Soc. 137(3) (2004), 551-557] conjectured that the pro-abelian group fH 1 (G;W n (O L))g n≥1 is isomorphic to zero. Hogadi and Pisolkar ['On the cohomology of Witt vectors of p-adic integers and a conjecture of Hesselholt', J. Number Theory 131(10) (2011), 1797-1807] have recently provided a proof of this conjecture. In this paper, we provide a simplified version of the original proof which avoids many of the calculations present in that version.

AB - Let K be a complete discrete valuation 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 = Gal(L=K) and suppose that the induced extension of residue fields k L=k K is separable. Let W n ( ) denote the ring of p-typical Witt vectors of length n. Hesselholt ['Galois cohomology of Witt vectors of algebraic integers', Math. Proc. Cambridge Philos. Soc. 137(3) (2004), 551-557] conjectured that the pro-abelian group fH 1 (G;W n (O L))g n≥1 is isomorphic to zero. Hogadi and Pisolkar ['On the cohomology of Witt vectors of p-adic integers and a conjecture of Hesselholt', J. Number Theory 131(10) (2011), 1797-1807] have recently provided a proof of this conjecture. In this paper, we provide a simplified version of the original proof which avoids many of the calculations present in that version.

KW - Galois cohomology

KW - Hesselholt's conjecture

KW - Witt vectors

KW - algebraic integers

UR - http://www.scopus.com/inward/record.url?scp=84869039631&partnerID=8YFLogxK

U2 - 10.1017/S0004972711003315

DO - 10.1017/S0004972711003315

M3 - Article

SN - 0004-9727

VL - 86

SP - 456

EP - 460

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 3

ER -