| Résume | Abstract: Intersection theory has proved to be a fundamental tool in
algebraic geometry, and as a consequence it has motivated analogous
theories such as arithmetic intersection geometry. In this
work-in-progress talk I will present a new intersection theory for norms
on rings using purely algebraic means. It provides a generalization and
at the same time a completely unified formulation of geometric and
arithmetic intersection theory for line bundles. I will also discuss
possible applications to other areas of mathematics, such as discrete
geometry or the theory of modular forms.
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