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36
On differential graded categories
 INTERNATIONAL CONGRESS OF MATHEMATICIANS. VOL. II
, 2006
"... Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, DuggerShipley,..., Toën and ToënVaquié. ..."
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Cited by 190 (4 self)
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Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, DuggerShipley,..., Toën and ToënVaquié.
Localization theorems in topological Hochschild homology and topological cyclic homology
, 2008
"... We construct localization cofiber sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of spectral categories. Using a “global ” construction of the THH and TC of a scheme in terms of the perfect complexes in a spectrally enriched version of the category of ..."
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We construct localization cofiber sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of spectral categories. Using a “global ” construction of the THH and TC of a scheme in terms of the perfect complexes in a spectrally enriched version of the category of unbounded complexes, the sequences specialize to localization cofiber sequences associated to the inclusion of an open subscheme. These are the targets of the cyclotomic trace from the localization sequence of ThomasonTrobaugh in Ktheory. We also deduce versions of Thomason’s blowup formula and the projective bundle formula for THH and TC.
Kregularity, cdhfibrant Hochschild homology, and a conjecture of Vorst
 J. Amer. Math. Soc
, 2006
"... Abstract. In this paper we prove that for an affine scheme essentially of finite type over a field F and of dimension d, Kd+1regularity implies regularity, assuming that the characteristic of F is zero. This verifies a conjecture of Vorst. ..."
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Abstract. In this paper we prove that for an affine scheme essentially of finite type over a field F and of dimension d, Kd+1regularity implies regularity, assuming that the characteristic of F is zero. This verifies a conjecture of Vorst.
Higher algebraic Ktheory (after Quillen, . . . )
, 2007
"... We give a short introduction (with a few proofs) to higher algebraic Ktheory (mainly of schemes) based on the work of Quillen, Waldhausen, Thomason and others. ..."
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Cited by 13 (0 self)
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We give a short introduction (with a few proofs) to higher algebraic Ktheory (mainly of schemes) based on the work of Quillen, Waldhausen, Thomason and others.
Infinitesimal cohomology and the Chern character to negative cyclic homology
, 2008
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Hermitian Ktheory, derived equivalences and Karoubi’s fundamental theorem
 arXiv:1209.0848
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A 1Homotopy of Chevalley Groups
, 2008
"... In this paper, we describe the sheaves of A1homotopy groups of a simplyconnected Chevalley group G. The A1homotopy group sheaves can be identified with the sheafification of the unstable KaroubiVillamayor Kgroups. ..."
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Cited by 10 (4 self)
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In this paper, we describe the sheaves of A1homotopy groups of a simplyconnected Chevalley group G. The A1homotopy group sheaves can be identified with the sheafification of the unstable KaroubiVillamayor Kgroups.
spectral sequences on singular schemes and failure of generalized Gersten conjecture
 Proceedings of the American Mathematical Society 137, no 1 (2009
"... Abstract. We construct a new localglobal spectral sequence for Thomason’s nonconnective Ktheory, generalizing the Quillen spectral sequence to possibly nonregular schemes. Our spectral sequence starts at the E1page where it displays Gerstentype complexes. It agrees with Thomason’s hypercohomo ..."
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Abstract. We construct a new localglobal spectral sequence for Thomason’s nonconnective Ktheory, generalizing the Quillen spectral sequence to possibly nonregular schemes. Our spectral sequence starts at the E1page where it displays Gerstentype complexes. It agrees with Thomason’s hypercohomology spectral sequence exactly when these Gerstentype complexes are locally exact, a condition which fails for general singular schemes, as we indicate. Our main result is the following application of abstract triangular geometry [2]. Theorem 1. Let X be a (topologically) noetherian scheme of finite Krull dimension. Then there exists a spectral sequence whose first page is
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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Cited by 9 (4 self)
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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.