E. Friedlander and M. Walker, Function spaces and continuous algebraic pairings for varieties, Comp. Math. 125 (2001), 69--110. Home/Search Document Details and Download
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Rational Isomorphisms between K-Theories and Cohomology.. - Friedlander, Walker Self-citation (Friedlander Walker) (Correct)
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E. Friedlander and M. Walker, Function spaces and continuous algebraic pairings for varieties, Comp. Math. 125 (2001), 69--110.
Semi-Topological K-Theory of Real VARIETIES - Friedlander, Walker Self-citation (Friedlander Walker) (Correct)
....then Mor k (X, G) coincides with Hom k (X w , G) the collection of morphisms of k varieties from X w to G. As in [FW1; 2] when k = C we impose a topology on MorC (X, G) resulting in a topological space which we will write as MorC (X, G) here (but which was written as Mor(X,G) an in [FW1]) We briefly recall the description of this topology so as to extend it to cover the case k = R. First, one chooses projective closures X # X SEMI TOPOLOGICAL K THEORY OF REAL VARIETIES 5 and G # G and then defines Y to be the Chow variety of cycles on X G of appropriate degree. Then E ....
....monoid. This gives some sense of the space KR semi (X) In Section 7 of this paper, we give a more explicit description of this space in terms of a mapping telescope. The natural map KR semi (X) # KR semi (X A 1 ) is a weak homotopy equivalence of spectra, since by the techniques of [FW1], for any real quasi projective varieties X and G, there is a continuous map A 1 (R) MorR (X A 1 , G) #MorR (X A 1 , G) sending (t, f) to f( t) This map shows that MorR (X, G) is a deformation retract of MorR (X A 1 , G) Thus the theory KR semi ( is homotopy ....
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E. Friedlander and M. Walker, Function spaces and continuous algebraic pairings for varieties, To appear in Comp. Math., available at http://www.math.uiuc.edu/Ktheory.
Semi-Topological K-Theory Using Function Complexes - Friedlander, Walker Self-citation (Friedlander Walker) (Correct)
....transition maps, just as were the pairings (2.2.1) Taking the direct limit over M and the inverse limit over N , we obtain the desired pairing. We now assume k = C in order to realize sets such as Mor(X; Grassn (P N ) as topological spaces; these spaces arise naturally using the results of [13]. Let (Sm=C ) 1 denote the category of smooth, affine varieties essentially of finite type over C having Krull dimension at most one (so that objects of (Sm=C ) 1 are localizations of smooth affine varieties over C ) For quasi projective complex varieties X, Y we let Mor(X;Y ) denote the ....
....from the category (Sm=C ) 1 to the category of sets, which sends C 2 (Sm=C ) 1 to the set Mor(C Theta X;Y ) of continuous algebraic maps from C Theta X to Y . When X is weakly normal, Mor(X;Y ) is nothing more than the functor Hom( Gamma Theta X;Y ) on (Sm=C ) 1 . Furthermore, as shown in [13], the functor Mor(X;Y ) admits a proper, constructible presentation that is, this functor is representable by a disjoin union of constructible subsets of projective space modulo a proper equivalence relation. Consequently, by [13; 2.4] the set Mor(X;Y ) admits a natural topology and we write ....
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E. Friedlander and M. Walker, Function spaces and continuous algebraic pairings for varieties, Preprint, available at http://www.math.uiuc.edu/K-theory.
Semi-Topological K-Theory Using Function Complexes - Friedlander, Walker Self-citation (Friedlander Walker) (Correct)
....transition maps, just as were the pairings (2.2.1) Taking the direct limit over M and the inverse limit over N , we obtain the desired pairing. We now assume k = C in order to realize sets such as Mor(X; Grassn (P N ) as topological spaces; these spaces arise naturally using the results of [13]. Let (Sm=C ) 1 denote the category of smooth, ane varieties essentially of nite type over C having Krull dimension at most one (so that objects of (Sm=C ) 1 are localizations of smooth ane varieties over C ) For quasi projective complex varieties X , Y we let Mor(X;Y ) denote the functor ....
....: Sm=C ) 1 (sets) from the category (Sm=C ) 1 to the category of sets, which sends C 2 (Sm=C ) 1 to the set Mor(C X;Y ) of continuous algebraic maps from C X to Y . When X is weakly normal, Mor(X;Y ) is nothing more than the functor Hom( X;Y ) on (Sm=C ) 1 . Furthermore, as shown in [13], the functor Mor(X;Y ) admits a proper, constructible presentation that is, this functor is representable by a disjoin union of constructible subsets of projective space modulo a proper equivalence relation. Consequently, by [13; 2.4] the set Mor(X; Y ) admits a natural topology and we write ....
[Article contains additional citation context not shown here]
E. Friedlander and M. Walker, Function spaces and continuous algebraic pairings for varieties, Preprint, available at http://www.math.uiuc.edu/K-theory.
Holomorphic K-Theory, Algebraic Co-Cycles, AND LOOP GROUPS - Cohen, Lima-Filho (1999) (Correct)
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E.M. Friedlander and M.E. Walker, Function spaces and continuous algebraic pairings for varieties, preprint, (1999). HOLOMORPHIC K -THEORY 37
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