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We prove a blow-up formula for cyclic homology which we use to show that infinitesimal K-theory satisfies cdh-descent. Combining that result with some computations of the cdh-cohomology of the sheaf of regular functions, we verify a conjecture of Weibel predicting the vanishing of algebraic K-theory of a scheme in degrees less than minus the dimension of… (More)
The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes called perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In particular, we have a characterization of faces of the sum in terms of the face lattice of a given… (More)
We present a tight bound on the exact maximum complexity of Minkowski sums of poly-topes in R 3. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m
We provide a patch to complete the proof of the Voevodsky-Rost Theorem, that the norm residue map is an isomorphism. (This settles the motivic Bloch-Kato conjecture).
The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes we call perfectly centered and the combinatorial properties of the Minkowski sum with their own dual. In particular, we have a characterization of face lattice of the sum in terms of the face lattice of a… (More)
It is known that in the Minkowski sum of r polytopes in dimension d, with r < d, the number of vertices of the sum can potentially be as high as the product of the number of vertices in each summand . However, the number of vertices for sums of more polytopes was unknown so far. In this paper, we study sums of polytopes in general orientations, and show… (More)
Consider a <i>routing problem</i> instance consisting of a <i>demand graph H</i> = (<i>V, E</i>(<i>H</i>)) and a <i>supply graph G</i> = (<i>V, E</i>(<i>G</i>)). If the pair obeys the cut condition, then the <i>flow-cut gap</i> for this instance is the minimum value <i>C</i> such that there exists a feasible multiflow for <i>H</i> if each edge of <i>G</i>… (More)
We give an axiomatic framework for proving that the norm residue map is an isomorphism (i.e., for settling the motivic Bloch-Kato conjecture). This framework is a part of the Voevodsky-Rost program.
Let G=(V,E) be a supply graph and H=(V,F) a demand graph defined on the same set of vertices. An assignment of capacities to the edges of G and demands to the edges of H is said to satisfy the <i>cut condition</i> if for any cut in the graph, the total demand crossing the cut is no more than the total capacity crossing it. The pair (G,H) is called… (More)
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