论文标题
固定点，局部单片和一致性覆盖的不可压缩性
Fixed points, local monodromy, and incompressibility of congruence covers
论文作者
论文摘要
我们证明了某些局部单组群在étale覆盖物上的作用的固定点定理，并使用它来推断基本维度的下限。特别是，我们提供了更多（但不是全部）Farb，Kisin和Wolfson的结果的更多几何证明，该结果使用算术方法证明了Shimura品种和模量曲线空间的不可压缩性结果。我们的方法使我们能够证明典型组的结果，以及减少模态的曲线和模量曲线空间的良好素数。
We prove a fixed point theorem for the action of certain local monodromy groups on étale covers and use it to deduce lower bounds in essential dimension. In particular, we give more geometric proofs of many (but not all) of the results of the preprint of Farb, Kisin and Wolfson, which uses arithmetic methods to prove incompressibility results for Shimura varieties and moduli spaces of curves. Our method allows us to prove results for exceptional groups, and also for the reduction modulo good primes of Shimura varieties and moduli spaces of curves.
