… In recent years some of the most exciting developments in Grothendieck duality have been
in the area of non-commutative geometry, and from the results of this paper it is possible to …

… The point of this article is that the Grothendieck duality is very easy to prove by homotopy …
But the reader is not assumed familiar with homotopy theory; hence the first few sections, in …

… an equivalence of the mock homotopy category of projectives with the homotopy category of
… interpreting Grothendieck duality as an equivalence of categories of unbounded complexes. …

… triangle-equivalences of Grothendieck duality over Ding-… some triangle equivalences
involving Grothendieck duality over … Let us give a simple background of Grothendieck duality and …

… is the homotopy category of pure injective flat quasi-coherent OX -modules. Where X is affine,
we show that this equivalence is the infinite completion of the Grothendieck duality theorem…

… : The pro-unipotent Grothendieck– Teichmüller group is isomorphic to the group of homotopy
… We also provide an account of the Koszul duality of operads in an appendix of this volume, “…

… duality formula. Serre … equivalences” in a rather obvious sense (NB the definition of the
Πi’s of an ∞-groupoid is practically trivial!), we get a category equivalent to the usual homotopy …

… of the field with one element”) is the stable homotopy category of connective spectra. We
also describe some basic features of Grothendieck duality for the map from Spec Z to Spec M0, …

… The point of this article is that Grothendieck duality is very easy to prove by homotopy … But
the reader is not assumed familiar with homotopy theory; hence the first few sections, in which …

… method of construction of duality in [RD] proceeds by developing a theory of the 6-functor f (…
The most fundamental proper smooth morphism in Grothendieck's approach to duality theory …