Existence of non-free stably free Swan module resolves Wall Problem A4 and yields homotopy inequivalent n-complexes after single vs multiple stabilizations when n ≡ 3 mod 4.
Jordan and Bjorn Poonen,The analytic class number formula for 1-dimensional affine schemes, Bull
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Swan modules and homotopy types after a single stabilisation
Existence of non-free stably free Swan module resolves Wall Problem A4 and yields homotopy inequivalent n-complexes after single vs multiple stabilizations when n ≡ 3 mod 4.