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arxiv: 1407.3765 · v2 · pith:SRROFBU4new · submitted 2014-07-14 · 🧮 math.KT

Notes on Triangulated Categories

Tobias Fritz This is my paper
classification 🧮 math.KT
keywords triangulatedcategoriesaxiomsalgebrabiproductsconcludecoveringderive
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We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms for triangulated categories and derive all other statements from these, including the existence of biproducts. We conclude with a list of examples.

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  1. Pro-$p$ Iwahori-Hecke modules in semisimple rank one and singularity categories

    math.RT 2026-04 unverdicted novelty 7.0

    Equivalence Ho(H_GL2) ≃ Sing(X_q,GL2) recovers Grosse-Klönne's mod-p Langlands correspondence for Hecke modules, with explicit descriptions of Ho(H_G) for SL2(F) and PGL2(F).