TL;DR
This paper provides a unified abstract framework for slope filtrations across various mathematical domains, highlighting deep connections and common properties among them.
Contribution
It introduces a general abstract approach to slope filtrations and surveys the interrelations between different concrete instances in diverse areas.
Findings
Unified treatment of slope filtrations across disciplines
Identification of common properties among various filtrations
New insights into the connections between different mathematical domains
Abstract
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of common properties. We propose a unified abstract treatment of slope filtrations, and survey how new ties between different domains have been woven by dint of deep correspondences between different concrete slope filtrations.
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Taxonomy
TopicsSoil erosion and sediment transport · Soil and Unsaturated Flow · Landslides and related hazards