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math.CT2018
Non-exactness of direct products of quasi-coherent sheaves
Ryo Kanda
For a noetherian scheme that has an ample family of invertible sheaves, we prove that direct products in the category of quasi-coherent sheaves are not exact unless the scheme is a…
math.CT2018
Extension groups between atoms in abelian categories
Ryo Kanda
We introduce the extension groups between atoms in an abelian category. For a locally noetherian Grothendieck category, the localizing subcategories closed under injective envelope…