nLab
standard conjectures on algebraic cycles

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

What are called the standard conjectures on algebraic cycles are several conjectures brought up by Grothendieck, concerned with the relation between algebraic cycles and Weil cohomology theories. The first (Lefschetz standard conjecture) is an existence assertion for algebraic cycles (Grothendieck - 68), the second (Hodge standard conjecture) is a statement of positivity, generalising Weil’s well-known positivity theorem in the theory of abelian varieties (Grothendieck - 68). They were also followed by “Beilinson's dream” on motivic (complexes of) sheaves which comprise what are called the standard conjectures of Beilinson.

References

Revised on August 28, 2014 05:50:41 by M. Carmona? (190.71.39.126)