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Results tagged with motives
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user 111491
for questions about motives in algebraic geometry, including constructions of categories of motives and motivic sheaves, and aspects of the standard conjectures.
3
votes
Are exotic affine spaces motivic/whatever equivalent to affine space?
Here is an argument showing that if $V$ is a smooth complex surface with trivial integral homology groups (note that exotic $\mathbf{A}^2$ do not exist, as explained in the comments), then $[V] = \mat …
- 2,310
11
votes
1
answer
873
views
K-equivalence ⇒ isomorphism of Chow motives?
Derived categories and Chow motives play the role of universal cohomology theories, in noncommutative, and commutative worlds respectively. … Do we expect that K-equivalence implies isomorphism of rational, or even integral Chow motives?
Example 1. Integral Chow motives of varieties related by a standard flop are isomorphic: Q. …
- 2,310
2
votes
Virtual Lefschetz motive
In characteristic zero, there is a canonical ring homomorphism from the Grothendieck ring of varieties to the Grothendieck ring of the additive tensor category of Chow motives (and the latter ring coincides … with the Grothendieck ring of the triangulated category of Voevovsky's motives by a result of Bondarko). …
- 2,310
4
votes
K-equivalence ⇒ isomorphism of Chow motives?
K-equivalence $\implies$ isomorphism of (rational) Chow motives is a conjecture going back to this 2002 paper of Wang (Conjecture 2.2); see this overview paper of his for what else K-equivalence should …
- 2,310