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.
@article{CML_2009__1_1_1_0,
author = {Andr\'e, Yves},
title = {Slope filtrations},
journal = {Confluentes Mathematici},
pages = {1--85},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {1},
number = {1},
year = {2009},
doi = {10.1142/S179374420900002X},
language = {en},
url = {http://archive.numdam.org/articles/10.1142/S179374420900002X/}
}
André, Yves. Slope filtrations. Confluentes Mathematici, Tome 1 (2009) no. 1, pp. 1-85. doi : 10.1142/S179374420900002X. http://archive.numdam.org/articles/10.1142/S179374420900002X/
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