Uniformizable families of tt-motives

Abelian $t$-modules and the dual notion of $t$-motives were introduced by Anderson as a generalization of Drinfeld modules. For such Anderson defined and studied the important concept of uniformizability. It is an interesting question, and the main objective of the present article to see how uniformizability behaves in families. Since uniformizability is an analytic notion, we have to work with families over a rigid analytic base. We provide many basic results, and in fact a large part of this article concentrates on laying foundations for studying the above question. Building on these, we obtain a generalization of a uniformizability criterion of Anderson and, among other things, we establish that the locus of uniformizability is Berkovich open.Comment: 40 pages, v2: Section 7 rewritten; to appear in Trans. Amer. Math. So

On local Galois deformation rings

We show that framed deformation rings of mod $p$ representations of the absolute Galois group of a $p$-adic local field are complete intersections of expected dimension. We determine their irreducible components and show that they and their special fibres are normal and complete intersection. As an application we prove density results of loci with prescribed $p$-adic Hodge theoretic properties.Comment: Revised version after a referee report. Lemma 3.21 has a better proof following a suggestion of the referee, and the appendix on Kummer-irreducible points has been rewritte

„Der Herr ist mein Hirte“ – Konzeptuelle Metapher als Lebenswirklichkeit

By means of metaphor, the less tangible can be made more tangible. This also applies to the declaration “The LORD is my shepherd” (Ps 23:1b). For a detailed approach to this declaration and the psalms, the focus here is first on conceptual perception (of God) and the Conceptual Metaphor Theory. It is then applied to the declaration, “The LORD is my shepherd,” unfolded in its radiant effect on the entire psalm and merged again into one. The aim is to prove that metaphorical conceptualisation makes the world shine in a new light and become experienceable, as the psalmist experienced in the encounter with God, making himself perceptible to him. Concretely, the psalmist explores the world of the Ancient Near East and of the confidential personal relationship between himself and God in the image of the shepherd-king and the human being-sheep. He underlines the covenant relationship between the Lord and the vassal – and thus the possibility of becoming a reality in one’s personal life. https://doi.org/10.17159/2312–3621/2021/v34n1a1