<\g> SO(3) Galois groups elliptic curves K3 surfaces degree 4 quartic quadratic GL(N) ζ(s) SO(N) degree: abelian surfaces GSp(4) degree d dimension 6 GL(1) degree 6 GSp(2) degree d Q sextic dimension 5 1 dimension 4 GL(5) dimension 3 dimension N 2 dimension 2 C-Y 3-folds GSp(2m) 5 genus 3 N GL(3) Q quintic 3 cubic hyperelliptic curves degree 5 degree 3 4 genus 2 6 L(s,χ) GSp(6) SO(2) degree 2 GL(6) SO(4) GL(4) GL(2)