After reviewing'some preliminary general nonsense, we discuss the basic formalism of the
functor f#: D qc+(Y)→ D qc (X)(resp. f D qc+(Y)→ D qc+(X)) for a smooth (resp. finite) map f …

We provide a proof of Nagata's compactification theorem: any separated map of finite type
between quasi-compact and quasi-separated schemes (eg, noetherian schemes) factors as …

In these expository notes derived categories and functors are gently introduced, and used
along with Koszul complexes to develop the basics of local cohomology. Local duality and …

We construct a “derived” version of Grothendieck's Quot scheme which is a dg-scheme, ie,
an object RQuot of a certain nonabelian right derived category of schemes. It has the …

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 …

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 …

Mathematische Annalen Page 1 DOI: 10.1007/s00208-005-0707-6 Math. Ann. 333, 859–931
(2005) Mathematische Annalen The logarithmic cotangent complex Martin C. Olsson …

An obstruction theory is developed to decide when an isomorphism of rational cohomology
can be realized by a rational homotopy equivalence (either between rationally nilpotent …

Let k be a field and Sm/k be the category of smooth schemes over k. In this paper we study
contravariant functors from the category Sm/k to additive categories equipped with transfer …

Transfer maps for fibrations and duality Page 1 COMPOSITIO MATHEMATICA JC BECKER DH
GOTTLIEB Transfer maps for fibrations and duality Compositio Mathematica, tome 33, no 2 …