Abstract.
We show the undecidability of the question of isomorphism of forms over a polynomial ring $ R[t_1,\ldots,t_n] $, assuming a hypothesis about units in certain quaternion rings. Assuming this, it follows that isomorphisms of modules, and of affine algebraic varieties over R are undecidable.
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In memory of Gian-Carlo Rota
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Kim, K.H., Roush, F.W. Results on undecidability of isomorphism of forms over polynomial rings. Algebra univers. 49, 179–189 (2003). https://doi.org/10.1007/s00012-003-1816-2
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DOI: https://doi.org/10.1007/s00012-003-1816-2