论文标题
P-ADIC DE RHAM协同学
Plectic structures in p-adic de Rham cohomology
论文作者
论文摘要
鉴于希尔伯特（Hilbert）的模块化形式，用于完全真实的字段$ f $，而Prime $ p $完全分为$ f $，$ f $ - eigenspace in $ p $ p $ -adic-adic de rham rham共同体学模块化品种具有部分过滤的家族和部分frobenius map，并由$ f $ $ p $ p $ p $ p $ f。 Nekovar和Scholl的一般Pletic猜想提出了将这些结构与依托共同体学进行比较的“ Plet型比较同构”。在某些温和的假设下，我们在情况下证明了这个猜想。对于一般$ f $，我们证明了一个较弱的陈述，这是猜想的有力证据，这表明plectic hodge过滤具有通过与部分frobenii的同时特征性相交的规范分裂。 （以纪念Jan Nekovar）
Given a Hilbert modular form for a totally real field $F$, and a prime $p$ split completely in $F$, the $f$-eigenspace in $p$-adic de Rham cohomology of the Hilbert modular variety has a family of partial filtrations and partial Frobenius maps, indexed by the primes of $F$ above $p$. The general plectic conjectures of Nekovar and Scholl suggest a "plectic comparison isomorphism" comparing these structures to etale cohomology. We prove this conjecture in the case $[F : \mathbf{Q}] = 2$ under some mild assumptions; and for general $F$ we prove a weaker statement which is strong evidence for the conjecture, showing that plectic Hodge filtration has a canonical splitting given by intersecting with simultaneous eigenspaces for the partial Frobenii. (In memory of Jan Nekovar)
