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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorJohn Baez
   • CommentTimeMay 17th 2022
   • PermaLink
   Author: John Baez
   Format: MarkdownItexAdded Jannsen's result on semisimplicity of numerical motives. <a href="https://ncatlab.org/nlab/revision/diff/pure+motive/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/pure+motive/28">v28</a>, <a href="https://ncatlab.org/nlab/show/pure+motive">current</a>

   Added Jannsen’s result on semisimplicity of numerical motives.

   diff, v28, current

2. • CommentRowNumber2.
   • CommentAuthorJohn Baez
   • CommentTimeMay 17th 2022
   • PermaLink
   Author: John Baez
   Format: MarkdownItex$A$ was being used in two different ways here: for Chow groups and for a coefficient ring. I've called the coefficient ring $R$ since $A$ is standard for Chow groups. <a href="https://ncatlab.org/nlab/revision/diff/pure+motive/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/pure+motive/28">v28</a>, <a href="https://ncatlab.org/nlab/show/pure+motive">current</a>

   $A$ was being used in two different ways here: for Chow groups and for a coefficient ring. I’ve called the coefficient ring $R$ since $A$ is standard for Chow groups.

   diff, v28, current

3. • CommentRowNumber3.
   • CommentAuthorJohn Baez
   • CommentTimeMay 17th 2022
   • PermaLink
   Author: John Baez
   Format: MarkdownItexExplained good properties of Chow and numerical motives. <a href="https://ncatlab.org/nlab/revision/diff/pure+motive/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/pure+motive/28">v28</a>, <a href="https://ncatlab.org/nlab/show/pure+motive">current</a>

   Explained good properties of Chow and numerical motives.

   diff, v28, current