ﻻ يوجد ملخص باللغة العربية
Using recent development in motivic infinite loop space theory, we offer short and conceptual reproofs of some conjectures of Voevodskys on the slice filtration using the birational geometry of Hilbert schemes. The original proofs were due to Marc Levine using very different methods, namely, the homotopy coniveau tower.
We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties in any characteristic, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topologic
Using results obtained from the study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to the revlex term order in the Hilbert sc
This paper is dedicated to triangulated categories endowed with weight structures (a new notion; D. Pauksztello has independently introduced them as co-t-structures). This axiomatizes the properties of stupid truncations of complexes in $K(B)$. We al
We show that if X is a toric scheme over a regular ring containing a field then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was known in characteristic 0. The affi
In this paper we reduce the generalized Hilberts third problem about Dehn invariants and scissors congruence classes to the injectivity of certain Chern--Simons invariants. We also establish a version of a conjecture of Goncharov relating scissors co