An analogue of Serre’s conjecture for a ring of distributions

Abstract

The set 𝒜 := 𝔺δ0+ 𝒟+′, obtained by attaching the identity δ0 to the set 𝒟+′ of all distributions on 𝕉 with support contained in (0, ∞), forms an algebra with the operations of addition, convolution, multiplication by complex scalars. It is shown that 𝒜 is a Hermite ring, that is, every finitely generated stably free 𝒜-module is free, or equivalently, every tall left-invertible matrix with entries from 𝒜 can be completed to a square matrix with entries from 𝒜, which is invertible.

Keywords

• hermite ring
• serre’s conjecture
• algebraic k-theory
• schwartz distribution theory
• primary 46f10
• secondary 19b10, 19k99, 46h05