L‐equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces
We construct non‐trivial L‐equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L‐equivalence for curves (necessarily over non‐algebraically closed fields) and provide a new bit of evidence for the conjectural relationship between L‐equivalence and derived equivalence.