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Tensors, multivectors, wedge products, multilinear maps, exterior (Grassmann) algebras.

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Tensor and Hom objects for finite flat group schemes

The answer to your question is 'no'. If there existed a tensor product for finite flat group scheme, there would exist one for $p$-divisible groups (over rings of integers of $p$-adic fields, for exam …
Mikhail Bondarko's user avatar