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

Volume 158 / 2013

Amit Hogadi, Supriya Pisolkar Acta Arithmetica 158 (2013), 165-171 MSC: Primary 11S25. DOI: 10.4064/aa158-2-4

Abstract

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 $n\geq 0$, let $W_n(\mathcal O_L)$ denote the ring of Witt vectors of length $n$ with coefficients in $\mathcal O_L$. We show that the proabelian group $\{H^1(G,W_n(\mathcal O_L))\}_{n\in \mathbb N}$ is zero. This is an equicharacteristic analogue of Hesselholt's conjecture, which was proved before when the discrete valued fields are of mixed characteristic.

Authors

  • Amit HogadiSchool of Mathematics
    Tata Institute of Fundamental Research
    Homi Bhabha Road
    Colaba, Mumbai 400005, India
    e-mail
  • Supriya PisolkarSchool of Mathematics
    Tata Institute of Fundamental Research
    Homi Bhabha Road
    Colaba, Mumbai 400005, India
    e-mail

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