group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
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.