论文标题
差异方程和高弗罗贝尼乌斯力量的专业化
Specialization of Difference Equations and High Frobenius Powers
论文作者
论文摘要
我们研究了配备了自动形态$σ$的有价值的领域，该$σ$在本地无限签约的意义上是$α\llσα$，全部$ 0 <α\inγ$。我们表明，评估理论的各种概念，例如Henselian和严格的Henselian Hulls，承认有意义的转化类似物。我们证明了规范的融合结果，并表现出了转化的野生冲突的方式，由托索控制于广义矢量组。从理论上讲，我们确定模型伴侣：它是可决定的，接受简单的公理化，并享受将量化器消除到代数界限的量词。 该模型伴侣被证明与代数封闭且非定程价值领域的Frobenius作用的极限理论一致。这为差异品种以前仅在特征零中可用的差异品种开辟了道路。首先，配备了杰出的Frobenius $ x \ mapsto x^{q} $的代数关闭的估值字段类是可决定的，在$ q $中是均匀的。
We study valued fields equipped with an automorphism $σ$ which is locally infinitely contracting in the sense that $α\llσα$ for all $0<α\inΓ$. We show that various notions of valuation theory, such as Henselian and strictly Henselian hulls, admit meaningful transformal analogues. We prove canonical amalgamation results, and exhibit the way that transformal wild ramification is controlled by torsors over generalized vector groups. Model theoretically, we determine the model companion: it is decidable, admits a simple axiomatization, and enjoys elimination of quantifiers up to algebraically bounded quantifiers. The model companion is shown to agree with the limit theory of the Frobenius action on an algebraically closed and nontrivially valued field. This opens the way to a motivic intersection theory for difference varieties that was previously available only in characteristic zero. As a first consequence, the class of algebraically closed valued fields equipped with a distinguished Frobenius $x\mapsto x^{q}$ is decidable, uniformly in $q$.
