Advanced Tilting Seminar

Summer semester 2024/2025

• February 24th - Linear topological rings, finite topology on endomorphism rings.
Relevant literature:
• Stacks Project tag 07E7, Link
• nLab page and references within, Link
• Tibor Szelem, On a topology in endomorphism rings of Abelian groups. Publ. Math. Debrecen 5 (1957): 1-4. Link - Seems to be the first appearance of "finite topology" in the literature.
• March 3rd - Complete and separated linear topological rings.
Relevant literature:
• Stacks Project tag 07E7, Link
• Tibor Szelem, On a topology in endomorphism rings of Abelian groups. Publ. Math. Debrecen 5 (1957): 1-4. Link
• March 10th - Endomorphism ring is complete, "Complete free modules" over complete linear rings, monadic definition of modules.
Relevant literature:
• Leonid Positselski, Contramodules, Link - Subsection 2.1.
• March 17th - Definition of a contramodule, some basic properties of the category of contramodules.
Relevant literature:
• Leonid Positselski, Contramodules, Link - Subsection 2.1.
• Jan Šťovíček and Leonid Positselski, The tilting-cotilting correspondence, Link - Sections 6.1 & 6.2
• March 24th - Abstract properties of the category of contramodules.
Relevant literature:
• Leonid Positselski, Contramodules, Link - Subsection 2.1.
• Jan Šťovíček and Leonid Positselski, The tilting-cotilting correspondence, Link - Sections 6.2 & 6.3
• Leonid Positselsky and Jiří Rosická, Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories, Link - Section 5.
• Leonid Positselsky, Answer to the following question at Mathoverflow, Link.
• Locally presentable categories on nLab, Link.
• Adjoint functor theorem on nLab, Link.
• March 31th - Cocomplete categories a with projective generator, equivalence between Add(M) and Proj(Ctra-End(M)).
Relevant literature:
• Jan Šťovíček and Leonid Positselski, The tilting-cotilting correspondence, Link - Sections 6.3 & 7.1