Intermediate Jacobians and the slice filtration

Mixed Intermediate Jacobians

The slice filtration and mixed Tate motives

Using the ”slice filtration”, defined by effectivity conditions on Voevodsky’s triangulated motives, we define spectral sequences converging to their motivic cohomology and étale motivic cohomology. These spectral sequences are particularly interesting in the case of mixed Tate motives as their E2-terms then have a simple description. In particular this yields spectral sequences converging to t...

Delta robot: inverse, direct, and intermediate Jacobians

In the context of a parallel manipulator, inverse and direct Jacobian matrices are known to contain information which helps us identify some of the singular configurations. In this article, we employ kinematic analysis for the Delta robot to derive the velocity of the end-effector in terms of the angular joint velocities, thus yielding the Jacobian matrices. Setting their determinants to zero, ...

Multiplicative Properties of the Slice Filtration

Introduction Let S be a Noetherian separated scheme of finite dimension, and let SH(S) denote the motivic stable homotopy category of Morel and Voevodsky. In order to get a motivic version of the Postnikov tower, Voevodsky [23] constructs a filtered family of triangulated subcategories of SH(S):

The Equivariant Slice Filtration: a Primer

We present an introduction to the equivariant slice filtration. After reviewing the definitions and basic properties, we determine the sliceconnectivity of various families of naturally arising spectra. This leads to an analysis of pullbacks of slices defined on quotient groups, producing new collections of slices. Building on this, we determine the slice tower for the Eilenberg-Mac Lane spectr...