Sato-Tate groups of some weight 3 motives

Abstract

We establish the group-theoretic classification of Sato-Tate groups of self-dual motives of weight 3 with rational coefficients and Hodge numbers h^{3,0} = h^{2,1} = h^{1,2} = h^{0,3} = 1. We then describe families of motives that realize some of these Sato-Tate groups, and provide numerical evidence supporting equidistribution. One of these families arises in the middle cohomology of certain Calabi-Yau threefolds appearing in the Dwork quintic pencil; for motives in this family, our evidence suggests that the Sato-Tate group is always equal to the full unitary symplectic group USp(4).

Minor edits to correct typos and address LMFDB modular form label changes

References in corpus (3)

• Sato-Tate distributions and Galois endomorphism modules in genus 2
• Sato-Tate distributions of twists of y^2=x^5-x and y^2=x^6+1
• Modularity of the Consani-Scholten quintic

Cited by in corpus (7)

• Sato-Tate groups of y^2=x^8+c and y^2=x^7-cx
• Sato-Tate groups of abelian threefolds: a preview of the classification
• Equidistribution, L-functions, and Sato-Tate groups
• The twisting Sato-Tate group of the curve $y^2=x^8-14x^4+1$
• Hypergeometric L-functions in average polynomial time
• Arithmetic and intermediate Jacobians of some rigid Calabi-Yau threefolds
• Sato-Tate groups of genus 2 curves