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On Harder-Narasimhan filtrations and their compatibility with tensor products (1703.08047v2)
Published 23 Mar 2017 in math.NT, math.CT, and math.MG
Abstract: We attach buildings to modular lattices and use them to develop a metric approach to Harder-Narasimhan filtrations. Switching back to a categorical framework, we establish an abstract numerical criterion for the compatibility of these filtrations with tensor products. We finally verify our criterion in three cases, one of which is new.
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