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Abstract: . We show how algebraic K-theory and related theories can be defined in terms of "algebraic mapping spaces" to appropriate ind-schemes. Keywords: algebraic K-theory, infinite loop space, Quot-schemes, \Gamma-space 1. Introduction For quasi-projective varieties X and Y over a ground field k, let P d (X; Y ) denote the full subcategory of the category of coherent sheaves on X \Theta Y consisting of those coherent sheaves F such that F is flat over X and the support of F maps properly to X with ... (Update)
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...as the geometric realization of the simplicial spectrum n 7 K(X n ) Proof. This is basically a special case of Theorem 3. 3 of [17], but in that paper Segal s notion of a space [30] is used to exhibit an in nite loop space structure on j Hom(X ; K 1 )j in lieu of the...
...realization of the simplicial spectrum n 7 K(X Theta Delta n ) Proof. This is basically a special case of Theorem 3. 3 of [17], but in that paper Segal s notion of a Gamma space [30] is used to exhibit an infinite loop space structure on j Hom(X Theta Delta ffl ; K...
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BibTeX entry: (Update)
D. Grayson and M. Walker, Geometric models for algebraic K-theory, Preprint, available at http://www.math.uiuc.edu/K-theory. http://citeseer.ist.psu.edu/grayson99geometric.html More
@misc{ grayson-geometric,
author = "D. Grayson and M. Walker",
title = "Geometric models for algebraic K-theory",
text = "D. Grayson and M. Walker, Geometric models for algebraic K-theory, Preprint,
available at http://www.math.uiuc.edu/K-theory.",
url = "citeseer.ist.psu.edu/grayson99geometric.html" }
Citations (may not include all citations):54 Higher algebraic K-theory (context) - Quillen - 1972
39 Categories and cohomology theories (context) - Segal - 1974
21 theory of generalized free products (context) - Waldhausen - 1978
17 homotopy theory of schemes - Morel, Voevodsky - 1998
16 Cohomological theory of presheaves with transfers - Voevodsky
9 Private Communication (context) - Friedlander
6 theory using function complexes (context) - Friedlander, Walker - 1999
5 Weight filtrations via commuting automorphisms - Grayson - 1995
5 The spectral sequence relating algebraic K-theory to motivic.. (context) - Friedlander, Suslin - 1999
3 theory and motivic cohomology of schemes (context) - Levine - 1999
1 Letter to Bruno Harris (context) - Suslin
1 Technique de construction et th'eor`em d'existence en geom`e.. (context) - Grothendieck - 1961
1 homology theory and algebraic K-theory (context) - Segal - 1977
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Motivic complexes and the K-theory of automorphisms - Walker (1997) (Correct)
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