Grothendieck proved that if $ f: X\longrightarrow Y $ is a proper morphism of nice schemes,
then $ Rf_* $ has a right adjoint, which is given as tensor product with the relative canonical …

Grothendieck proved that if $ f: X\longrightarrow Y $ is a proper morphism of nice schemes,
then $ Rf_* $ has a right adjoint, which is given as tensor product with the relative canonical …

We give several related versions of global Grothendieck Duality for unbounded complexes
on noetherian formal schemes. The proofs, based on a non-trivial adaptation of Deligne's …

We give several related versions of global Grothendieck Duality for unbounded complexes
on noetherian formal schemes. The proofs, based on a nontrivial adaptation of Deligne's …

We present a sheafified derived-category generalization of Greenlees-May duality (a far-
reaching generalization of Grothendieck's local duality theorem): for a quasi-compact …

We study dualizing complexes. The unusual feature is that we do not assume them to have
bounded injective resolutions; we prove that the theory works just fine with no boundedness …

The article primarily surveys work that followed from the formulas discovered by Avramov
and Iyengar in 2008, which permit one to compute certain Hochschild homology and …

For a closed subscheme Z of a noetherian separated scheme X, let ΓZ be the functor of
sections with support in Z, taking OX-modules to OX-modules. Inspired by a theorem of …

An algebraic structure A (eg an associative algebra, a commutative algebra, an operad, etc.)
in the category of chain complexes is said to be formal if it is connected to its homology H (A) …

Let R be a ring. We prove that the homotopy category K (R-Proj) is always \aleph_1-
compactly generated, and, depending on the ring R, it may or may not be compactly …