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I am reading this paper on the complex multiplication of K3 surfaces. It seems that this is only defined for complex K3 surfaces, or K3 surfaces over number fields. Is there a more general defintion ...

Let $K$ be a finite extension field of $\mathbb{Q}_p$. Let us consider a semiabelian variety $G$ defined over $K$, i.e there exists an extension of an abelian variety $B$ and a torus $T$ defined over $...

In Matthias Wulkau's exposition of Scholze's thesis, the term perfectoid field is defined as follows: Let $K$ be a field endowed with a non-archimedian absolute value $\lvert\cdot\rvert$, and let $\...