论文标题
$ P $的派生的Hecke Action和普通的$ p $ -ADIC算术歧管
Derived Hecke action at $p$ and the ordinary $p$-adic cohomology of arithmetic manifolds
论文作者
论文摘要
我们研究了$ p $ $ p $的派生$ p $ p $ - adic-adic cromology of Mathrm G（\ Mathbb Q）$的算术亚组$ \ Mathrm g（\ Mathbb Q）$，即，我们研究了HIDA的普通Hecke Algebras的衍生版本。这是Venkatesh在Tame Case中研究的派生的Hecke动作的$ \ ell = P $的模拟。我们表明，在$ p $的派生的Hecke动作的特性与Galois共同体中的深层猜想有关，Galois共同体是经典Leopoldt猜想的较高类似物。
We study the derived Hecke action at $p$ on the ordinary $p$-adic cohomology of arithmetic subgroups of semisimple groups $\mathrm G(\mathbb Q)$, i.e., we study the derived version of Hida's theory for ordinary Hecke algebras. This is the analog at $\ell=p$ of derived Hecke actions studied by Venkatesh in the tame case. We show that properties of the derived Hecke action at $p$ are related to deep conjectures in Galois cohomology which are higher analogs of the classical Leopoldt conjecture.
