Remarks on Grothendieck's standard conjectures

TL;DR

This paper discusses how Grothendieck's standard conjectures are logically implied by two other conjectures in the realm of motives, connecting different foundational hypotheses in algebraic geometry.

Contribution

It establishes that Grothendieck's standard conjectures follow from the existence of a motivic t-structure or a weak form of Suslin's Lawson homology conjecture.

Findings

Grothendieck's conjectures are implied by the motivic t-structure conjecture.

Grothendieck's conjectures are implied by a weak form of Suslin's Lawson homology conjecture.

The paper links different motivic conjectures, suggesting a unified underlying framework.

Abstract

We show that Grothendieck's standard conjectures are implied by either of two other motivic conjectures: (a) by that of the existence of the motivic t-structure, and (b) by (a weak form of) Suslin's Lawson homology conjecture.