|
|
|
||
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (18.09.2023)
|
|
||
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (18.09.2023)
The final exam will be an oral exam. For zápočet, students will have to get 50% of marks on 3 homework assignments. |
|
||
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (18.09.2023)
(1) H. Krause. Localization theory for triangulated categories. In Triangulated categories, volume 375 of London Math. Soc. Lecture Note Ser., pages 161-235. Cambridge Univ. Press, Cambridge, 2010
(2) H. Krause. Homological theory of representations, volume 195 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2022
(3) M. Hovey, J. H. Palmieri, and N. P. Strickland. Axiomatic stable homotopy theory. Mem.Amer. Math. Soc., 128(610):x+114, 1997
(4) T. Barthel, D. Heard, and G. Valenzuela. Local duality in algebra and topology. Adv. Math., 335:563-663, 2018
(5) W. G. Dwyer and J. P. C. Greenlees. Complete modules and torsion modules. Amer. J. Math., 124(1):199-220, 2002 |
|
||
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (18.09.2023)
The course will give an introduction to triangulated categories, before turning to introducing local cohomology, firstly in the classical algebraic setting, and then in the triangulated realm and explaining how the latter recovers and generalises the former. We will then turn to exploring local duality in thetriangulated setting, which naturally leads us to consider other duality theorems such as Greenlees-May duality, and Warwick duality. We will show how one can recover the classical statement of Grothendieck local duality from this more general triangulated version. • Introduction to duality (1 lecture):
• Triangulated categories (6 lectures):
• Local cohomology in algebra (2 lectures):
• Local cohomology in triangulated categories (4 lectures):
• Duality theorems in triangulated categories (3 lectures):
|
|
||
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (18.09.2023)
Some familiarity with the following would be preferable, although we will review key aspects throughout the course as they become relevant. • Category theory: categories, functors, natural transformations, adjoints, Yoneda, (co)limits • Homological algebra: complexes, homology, derived functors |