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Register a new userGabber presentation lemma over noetherian domains
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Following Schmidt and Strunk, we give a proof of Gabber presentation lemma over a noetherian domain with infinite residue fields.
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We give a proof of Gabbers presentation lemma for finite fields. We use ideas from Poonens proof of Bertinis theorem to prove this lemma in the special case of open subsets of the affine plane. We then reduce the case of general smooth varieties to this special case.
In this paper, we study equivalences between the categories of quasi-coherent sheaves on non-commutative noetherian schemes. In particular, give a new proof of Caldararus conjecture about Morita equivalences of Azumaya algebras on noetherian schemes. Moreover, we derive necessary and sufficient condition for two reduced non-commutative curves to be Morita equivalent.
We describe new classes of noetherian local rings $R$ whose finitely generated modules $M$ have the property that $Tor_i^R(M,M)=0$ for $igg 0$ implies that $M$ has finite projective dimension, or $Ext^i_R(M,M)=0$ for $igg 0$ implies that $M$ has finite projective dimension or finite injective dimension.
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