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Tensor products of valued fields

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yaacov, ita¨ı ben

We give a short argument why the tensor product semi-norm on K ⊗k L is multiplicative when k is an algebraically closed valued field and K and L are valued extensions (valued in R). When the valuation on k is non-trivial we use the fact that ACVF, the theory of algebraically closed (non-trivially) valued fields, has quantifier elimination.

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