The sheaf of outer functions in the polydisc

Sergio Eduardo Zarantonello

Vol. 76 (1978), No. 1, 267–281

DOI: 10.2140/pjm.1978.76.267

Abstract

Let Uⁿ be the unit polydisc in Cⁿ. Define a presheaf by assigning to each relatively open subset W of Uⁿ the multiplicative group of outer functions in the intersection W ∩ Uⁿ. If 𝒬 denotes the associated sheaf, we prove that H^q(Uⁿ,𝒬) = 0 for all integers q ≧ 1.

Mathematical Subject Classification 2000

Primary: 32C35

Secondary: 32E30

Milestones

Received: 7 July 1977

Revised: 14 October 1977

Published: 1 May 1978