Весовые методы в некоммутативной геометрии Соснило Владимир Александрович

Короткий опис

Соснило, Владимир Александрович.
Весовые методы в некоммутативной геометрии = Weighted methods in Noncommutative geometry : Weighted methods in Noncommutative geometry : диссертация ... кандидата физико-математических наук : 01.01.06 / Vladimir Sosnilo; [Место защиты: ФГАОУ ВО «Национальный исследовательский университет «Высшая школа экономики»]. - Москва, 2021. - 94 с. : ил.
Оглавление диссертациикандидат наук Соснило Владимир Александрович
Contents
Introduction
Weight structures
1. Summary of results
1.1. Weight structures
1.2. Reconstruction theorem for weighted categories
1.3. Regular stacks
1.4. Theorem of Dundas-Goodwillie-McCarthy for weight structures
1.5. Categorical Milnor excision and pro-excision
1.6. Applications to stacks
2. On additive ^-categories
2.1. Basics
2.2. Verdier quotients
2.3. Idempotents
2.4. Exact sequences
3. Weight structures
3.1. Basics
3.2. From additive ^-categories to stable ^-categories via weights
3.3. Examples
4. Regularity
4.1. Regular ring spectra
4.2. Regular spectral stacks
4.3. Adjacent structures
4.4. Gluing weight structures
5. Nilpotent extensions via weights
5.1. Nilpotent extensions of additive ^-categories
5.2. Localizing invariants
5.3. Morita theory for additive ^-categories
5.4. The DGM theorem for weighted stable ^-categories and examples
6. Milnor excision for stable ^-categories and equivalences of pro-w-categories
6.1. The base change morphism
6.2. Milnor excision results
6.3. Pro-w-categories
6.4. Pro-Milnor squares
7. Applications to localizing invariants of ANS stacks
7.1. ANS stacks
7.2. Dimension of algebraic stacks
7.3. Localizing invariants of algebraic stacks
7.4. Equivariant pro-descent
7.5. Proof of pro-cdh-descent
7.6. Proof of the Weibel's conjecture
7.7. Applications to truncating invariants of stacks
7.8. Applications to the lattice conjecture 89 Conclusion 90 References