We attach buildings to modular lattices of finite length and show that they yield a natural framework for a metric version of the Harder-Narasimhan formalism. We establish a sufficient condition for the compatibility of Harder-Narasimhan filtrations with tensor products and verify our criterion in various cases coming from -adic Hodge theory.
@article{CML_2018__10_2_3_0, author = {Christophe Cornut}, title = {On {Harder-Narasimhan} filtrations and their compatibility with tensor products}, journal = {Confluentes Mathematici}, pages = {3--49}, publisher = {Institut Camille Jordan}, volume = {10}, number = {2}, year = {2018}, doi = {10.5802/cml.49}, mrnumber = {3928223}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.49/} }
TY - JOUR AU - Christophe Cornut TI - On Harder-Narasimhan filtrations and their compatibility with tensor products JO - Confluentes Mathematici PY - 2018 SP - 3 EP - 49 VL - 10 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.49/ DO - 10.5802/cml.49 LA - en ID - CML_2018__10_2_3_0 ER -
%0 Journal Article %A Christophe Cornut %T On Harder-Narasimhan filtrations and their compatibility with tensor products %J Confluentes Mathematici %D 2018 %P 3-49 %V 10 %N 2 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.49/ %R 10.5802/cml.49 %G en %F CML_2018__10_2_3_0
Christophe Cornut. On Harder-Narasimhan filtrations and their compatibility with tensor products. Confluentes Mathematici, Volume 10 (2018) no. 2, pp. 3-49. doi : 10.5802/cml.49. https://cml.centre-mersenne.org/articles/10.5802/cml.49/
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