A_inf具有不可数的克鲁尔维数

完美oid Tate代数具有不可数Krull维数

The perfectoid Tate algebra has uncountable Krull dimension

本文通过引入牛顿多边形形式体系并构造非标准变体，证明了完美oid Tate代数具有不可数素理想链，从而具有不可数Krull维数，并将结论推广到多变量情形。

Formalising the Krull Topology in Lean

The Galois group of an infinite Galois extension has a natural topology, called the Krull topology, which has the important property of being profinite. It is impossible to talk about Galois representations, and hence the Langlands Program, without first defining the Krull topology. We explain our formalisation of this topology, and our proof that it is profinite, in the Lean 3 theorem prover.

Characteristic ideals and Iwasawa theory

Let $Ł$ be a non-noetherian Krull domain which is the inverse limit of noetherian Krull domains $Ł_d$ and let $M$ be a finitely generated $Ł$-module which is the inverse limit of $Ł_d$-modules $M_d\,$. Under certain hypotheses on the rings $Ł_d$ and on the modules $M_d\,$, we define a pro-characteristic ideal for $M$ in $Ł$, which should play the role of the usual characteristic ideals for finitely generated modules over noetherian Krull domains. We apply this to the study of Iwasawa modules (in particular of class groups) in a non-noetherian Iwasawa algebra $\Z_p[[\Gal(\calf/F)]]$, where $F$ …

Specialization Method in Krull Dimension two and Euler System Theory over Normal Deformation Rings

The aim of this article is to establish the specialization method on characteristic ideals for finitely generated torsion modules over a complete local normal domain R that is module-finite over $O[[x_1, ..., x_d]]$, where $O$ is the ring of integers of a finite extension of the field of p-adic integers $Q_p$. The specialization method is a technique that recovers the information on the characteristic ideal $char_R(M)$ from $char_{R/I}(M/IM)$, where I varies in a certain family of nonzero principal ideals of R. As applications, we prove Euler system bound over Cohen-Macaulay normal domains by …

$\mathbf{A}_{\text{inf}}$ is infinite dimensional

Given a perfect valuation ring $R$ of characteristic $p$ that is complete with respect to a rank-$1$ nondiscrete valuation, we show that the ring $\mathbf{A}_{\text{inf}}$ of Witt vectors of $R$ has infinite Krull dimension.

关于Lagrange值恰好为3的无理数

On irrationals with Lagrange value exactly 3

本文证明了Lagrange值恰好为3的无理数集合X_3是不可数的，并进一步展示了具有特定解数的此类集合也是不可数的。