Algebraic cycles and higher K-theory
نویسندگان
چکیده
منابع مشابه
Algebraic Cycles and Completions of Equivariant K-theory
Let G be a complex, linear algebraic group acting on an algebraic space X . The purpose of this paper is to prove a Riemann-Roch theorem (Theorem 5.5) which gives a description of the completion of the equivariant Grothendieck group G0(G,X)⊗ C at any maximal ideal of the representation ring R(G) ⊗ C in terms of equivariant cycles. The main new technique for proving this theorem is our non-abeli...
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Here BΓ is the classifying space of the group Γ, and we denote by K−∞(R) the non-connective algebraic K-theory spectrum of the ring R. The homotopy groups of this spectrum are denoted Kn(R) and coincide with Quillen’s algebraic K-groups of R [Qui73] in positive dimensions and with the negative K-groups of Bass [Bas68] in negative dimensions. The homotopy groups of the spectrum X+∧K(R) are denot...
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We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, M∞-stable, homotopy-invariant, excisive Ktheory of algebras over a fixed unital ground ring H, (A, B) 7→ kk∗(A, B), which is universal in the sense that it maps uniquely to any other such theory. It turns out kk is related to C. Weibel’s homotopy algebraic K-theory, KH....
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We show how methods from K-theory of operator algebras can be applied in a completely algebraic setting to define a bivariant, M∞-stable, homotopy-invariant, excisive Ktheory of algebras over a fixed unital ground ring H, (A, B) 7→ kk∗(A, B), which is universal in the sense that it maps uniquely to any other such theory. It turns out kk is related to C. Weibel’s homotopy algebraic K-theory, KH....
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The antique origins of Algebraic Geometry lie in the study of solution sets of polynomial equations, in which complex, symplectic, and arithmetic geometry are bound tightly together. Many of the most spectacular recent developments in the subject have occurred through the consideration of these aspects in tandem: for example, the duality between symplectic and complex geometry that is mirror sy...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1986
ISSN: 0001-8708
DOI: 10.1016/0001-8708(86)90081-2