Results 1  10
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16
Cyclic homology, cdhcohomology and negative Ktheory
, 2005
"... We prove a blowup formula for cyclic homology which we use to show that infinitesimal Ktheory satisfies cdhdescent. Combining that result with some computations of the cdhcohomology of the sheaf of regular functions, we verify a conjecture of Weibel predicting the vanishing of algebraic Ktheor ..."
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We prove a blowup formula for cyclic homology which we use to show that infinitesimal Ktheory satisfies cdhdescent. Combining that result with some computations of the cdhcohomology of the sheaf of regular functions, we verify a conjecture of Weibel predicting the vanishing of algebraic Ktheory of a scheme in degrees less than minus the dimension of the scheme, for schemes essentially of finite type over a field of characteristic zero.
The nilpotence conjecture in Ktheory of toric varieties
, 2002
"... It is shown that all nontrivial elements in higher Kgroups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine toric varieties. ..."
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Cited by 9 (4 self)
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It is shown that all nontrivial elements in higher Kgroups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine toric varieties.
Infinitesimal cohomology and the Chern character to negative cyclic homology
, 2008
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Comparison between algebraic and topological Ktheory of locally convex algebras
, 2006
"... This paper is concerned with the algebraic Ktheory of locally convex Calgebras stabilized by operator ideals, and its comparison with topological Ktheory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological Ktheory agree on the compl ..."
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This paper is concerned with the algebraic Ktheory of locally convex Calgebras stabilized by operator ideals, and its comparison with topological Ktheory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological Ktheory agree on the completed projective tensor product Lˆ⊗J, and that the obstruction for the comparison map K(Lˆ⊗J) → Ktop (Lˆ⊗J) to be an isomorphism is (absolute) algebraic cyclic homology. We prove the existence of an exact sequence (Theorem 6.2.1) K top
THE KTHEORY OF TORIC VARIETIES
"... Abstract. Recent advances in computational techniques for Ktheory allow us to describe the Ktheory of toric varieties in terms of the Ktheory of fields and simple cohomological data. 1. ..."
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Abstract. Recent advances in computational techniques for Ktheory allow us to describe the Ktheory of toric varieties in terms of the Ktheory of fields and simple cohomological data. 1.
Cyclic homology of Hunital (pro)algebras, Lie algebra homology of matrices and a paper of Hanlon’s. Preprint. Available at http://arxiv.org/abs/math.KT/0504148
"... Abstract. We consider algebras over a field k of characteristic zero. The article is concerned with the isomorphism of graded vectorspaces H(gl(A)) ∼ → ∧(HC(A)[−1]) between the Lie algebra homology of matrices and the free graded commutative algebra on the cyclic homology of the kalgebra A, shift ..."
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Abstract. We consider algebras over a field k of characteristic zero. The article is concerned with the isomorphism of graded vectorspaces H(gl(A)) ∼ → ∧(HC(A)[−1]) between the Lie algebra homology of matrices and the free graded commutative algebra on the cyclic homology of the kalgebra A, shifted down one degree. For unital algebras this isomorphism is a classical result obtained by Loday and Quillen and independently by Tsygan. For Hunital algebras, it is known to hold too, as is that the proof follows from results of Hanlon’s. However, to our knowledge, the proof is not immediate, and has not been published. In this paper we fill this gap in the literature by offering a detailed proof. Moreover we establish the isomorphism in the general setting of (Hunital) proalgebras. 1.
The Steinberg group of a monoid ring, nilpotence, and algorithms
 J. Algebra
"... Abstract. For a regular ring R and an affine monoid M the homotheties of M act nilpotently on the Milnor unstable groups of R[M]. This strengthens the K2 part of the main result of [G5] in two ways: the coefficient field of characteristic 0 is extended to any regular ring and the stable K2group is ..."
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Abstract. For a regular ring R and an affine monoid M the homotheties of M act nilpotently on the Milnor unstable groups of R[M]. This strengthens the K2 part of the main result of [G5] in two ways: the coefficient field of characteristic 0 is extended to any regular ring and the stable K2group is substituted by the unstable ones. The proof is based on a polyhedral/combinatorial technique, computations in Steinberg groups, and a substantially corrected version of an old result on elementary matrices by Mushkudiani [Mu]. A similar stronger nilpotence result for K1 and algorithmic consequences for factorization of high Frobenius powers of invertible matrices are also derived. 1.
FLAT MODEL STRUCTURES FOR NONUNITAL ALGEBRAS AND HIGHER KTHEORY
, 906
"... Abstract. We prove the existence of a Quillen Flat Model Structure in the category of unbounded complexes of hunitary modules over a nonunital ring (or a kalgebra, with k a field). This model structure provides a natural framework where a Moritainvariant homological algebra for these nonunital ri ..."
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Abstract. We prove the existence of a Quillen Flat Model Structure in the category of unbounded complexes of hunitary modules over a nonunital ring (or a kalgebra, with k a field). This model structure provides a natural framework where a Moritainvariant homological algebra for these nonunital rings can be developed. And it is compatible with the usual tensor product of complexes. The Waldhausen category associated to its cofibrations allows to develop a Morita invariant excisive higher Ktheory for nonunital algebras. 1. Introduction. Let A be a nonunital algebra (or ring). A classical question in Homotopy Theory is to find a ’good definition ’ of Ktheory and cyclic type homology for this type of rings and algebras. Namely, it is always possible to embed a nonunital ring A as a twosided ideal of a unital ring R (for instance, by choosing Ã = Z ⋉ A to be