Let C be a complex smooth projective algebraic curve endowed with an action of a finite group G such that the quotient curve has genus at least 3. We prove that if the G-curve C is very general for these properties, then the natural map from the group algebra \({{\mathbb {Q}}}G\) to the algebra of \({{\mathbb {Q}}}\)-endomorphisms of its Jacobian is an isomorphism. We use this to obtain (topological) properties regarding certain virtual linear representations of a mapping class group. For example, we show that the connected component of the Zariski closure of such a representation often acts \({{\mathbb {Q}}}\)-irreducibly in a G-isogeny space of \(H^1(C; {{\mathbb {Q}}})\) and with image a \({{\mathbb {Q}}}\)-almost simple group.

设C是一条复杂的光滑射影代数曲线，赋予有限群G的作用，使得商曲线至少有 3。我们证明，如果G曲线C对于这些性质非常普遍，那么自然映射来自群代数\({{\mathbb {Q}}}G\)到\({{\mathbb {Q}}}\) 的代数 - 其雅可比矩阵的自同构是同构。我们使用它来获得关于映射类组的某些虚拟线性表示的（拓扑）属性。例如，我们表明这种表示的 Zariski 闭包的连通分量通常在G 中不可约地作用于\({{\mathbb {Q}}}\)- \(H^1(C; {{\mathbb {Q}}})\) 的同构空间和图像\({{\mathbb {Q}}}\) - 几乎是简单的组。