Fix a symplectic K3 surface X homologically mirror to an algebraic K3 surface Y by an equivalence taking a graded Lagrangian torus L in X to the skyscraper sheaf of a point y of Y. We show there are Lagrangian tori with vanishing Maslov class in X whose class in the Grothendieck group of the Fukaya category is not generated by Lagrangian spheres. This is mirror to a statement about the `Beauville--Voisin subring' in the Chow groups of Y, and fits into a conjectural relationship between Lagrangian cobordism and rational equivalence of algebraic cycles.

中文翻译：

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K3 曲面上的有理等价和拉格朗日圆环

通过将 X 中的分级拉格朗日环面 L 与 Y 的 y 点的摩天大楼层等价，将辛 K3 曲面 X 同调地镜像到代数 K3 曲面 Y。格洛腾迪克群中的 Fukaya 范畴不是由拉格朗日球体产生的。这反映了 Y 的 Chow 群中关于“Beauville--Voisin 子环”的陈述，并且符合拉格朗日协边和代数环的有理等价之间的推测关系。