34 pages matching nonsingular variety in this book
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Real algebraic cycles
The Galois action
21 other sections not shown
A-Wlod(X action of G acts trivially algebraic cycles algebraic variety algebraic variety defined bifunctor Borel-Moore homology bounded below complex canonical isomorphism cap product CHk(X codimension coefficients cohomological dimension cohomology manifold commutative diagram commutative ring complex algebraic variety composite mapping connected component Corollary definition denoted derived category divisor edge morphism equivalent to zero equivariant Borel-Moore homology equivariant cohomology equivariant cycle map example finite cohomological dimension flat fundamental class G A modules G action G acts G sheaves G space G-A-module geometrically irreducible variety hence Hochschild-Serre spectral sequence homomorphism Ht(X implies induces an isomorphism injective involution irreducible variety Lemma Let G line bundle locally compact space long exact sequence nonsingular variety notation orientation Pic(X Poincare duality Proof proper push-forward Proposition quasi-isomorphism quasi-morphism rationally equivalent real algebraic variety real algebraically equivalent real cycle map real Enriques surface restriction Section sheaf short exact sequence subgroup subspace subvariety surjective Theorem topological