… the fundamental class of a flat map f : X → Y of S-schemes x : X → S , y : Y → S as above.
Having fixed S, we'll often set δ X : = δ x , H X : = H x . With such notation, the fundamental class …

… Serre duality on normal projective varieties; and shortly thereafter, into Grothendieck duality
… expressed locally via residues and globally via the fundamental class of V/k. (These notions …

… All these facts should fit into a general theory of the fundamental class of an arbitrary separated
finite-type flat map ƒ: X →Y with d-dimensional fibers, a canonical derived-category map …

… into Algebraic Geometry in Serre’s fundamental paperu“, and it … obtained by means of a local
duality theory, which seems to … get that formation of characteristic classes is compatible with …

… set of isomorphism class representatives for the quasi-coherent sheaves of type r,, the …
The most fundamental proper smooth morphism in Grothendieck's approach to duality theory is …

… complex concerned is fundamental; it … class of local rings which possess dualizing complexes,
it is desirable to have the local duality theorem available for local rings in the latter class. …

… Global “geometric” class field theory as a cohomological duality formula… fundamental
groupoid embodies the 1-truncated homotopy type. For two spaces X,Y, the set of homotopyclasses …

… Grothendieck’s fundamental insight is that this problem can be bypassed by considering …
Given an algebraic structure A we can consider a certain class of representations of A, that is …

… outstanding features of Grothendieck duality is the … Grothendieck operations, and a web of
relations among them (see, eg, [L3]). These two aspects are linked by the fundamental class of …

… duality to a canonical version of Grothendieck duality for … duality is drawn via fiat base change
(ž5.4)- for which, incidentally, Greenlees-May duality is essentialand the fundamental class …