Poslední úprava: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (30.05.2023)
Jednorázová výběrová přednáška na různá témata.
Poslední úprava: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (05.01.2024)
Non-repeated universal elective course.
In the academic year 2023/24:
This course will be about Cohen–Macaulay modules over local Cohen–Macaulay rings, with a view
towards Auslander-Reiten sequences and what it means for such sequences to generate the relations of
the Grothendieck group
Podmínky zakončení předmětu
Poslední úprava: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (10.06.2019)
Předmět je zakončen ústní zkouškou.
Literatura -
Poslední úprava: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (05.01.2024)
(1) M. Auslander, Isolated singularities and existence of almost split sequences, in: Representation
Theory, II, Ottawa, Ont., 1984, in: Lecture Notes in Math., vol. 1178, Springer, Berlin, 1986.
(2) ] M. Auslander, Representation theory of Artin algebras II, Comm. Algebra 1 (1974) 269-310.
(3) M. Auslander, Relations for Grothendieck groups of Artin algebras, Proc. Amer. Math. Soc. 91
(3)(1984) 336-340.
(4) M. Auslander, I. Reiten, Grothendieck groups of algebras and orders, J. Pure Appl. Algebra 39
(1-2) (1986) 1-51.
(5) Y. Yoshino, Cohen-Macaulay Modules over Cohen-Macaulay Rings, London Mathematical Society Lecture Note Series, vol. 146, Cambridge University Press, Cambridge, 1990.
(6) T. Kobayashi, Syzygies of Cohen-Macaulay modules and Grothendieck groups, J. Algebra 490
(2017) 372-379.
(7) H. Enomoto; Classifications of exact structures and Cohen-Macaulay-finite algebras, Advances
in Mathematics Volume 335, 7 September 2018, Pages 838-877.
(8) H. Enomoto; Relations for Grothendieck groups and representation-finiteness; Journal of Algebra
Volume 539, 1 December 2019, Pages 152-176.
Poslední úprava: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (05.01.2024)
(1) M. Auslander, Isolated singularities and existence of almost split sequences, in: Representation
Theory, II, Ottawa, Ont., 1984, in: Lecture Notes in Math., vol. 1178, Springer, Berlin, 1986.
(2) ] M. Auslander, Representation theory of Artin algebras II, Comm. Algebra 1 (1974) 269-310.
(3) M. Auslander, Relations for Grothendieck groups of Artin algebras, Proc. Amer. Math. Soc. 91
(3)(1984) 336-340.
(4) M. Auslander, I. Reiten, Grothendieck groups of algebras and orders, J. Pure Appl. Algebra 39
(1-2) (1986) 1-51.
(5) Y. Yoshino, Cohen-Macaulay Modules over Cohen-Macaulay Rings, London Mathematical Society Lecture Note Series, vol. 146, Cambridge University Press, Cambridge, 1990.
(6) T. Kobayashi, Syzygies of Cohen-Macaulay modules and Grothendieck groups, J. Algebra 490
(2017) 372-379.
(7) H. Enomoto; Classifications of exact structures and Cohen-Macaulay-finite algebras, Advances
in Mathematics Volume 335, 7 September 2018, Pages 838-877.
(8) H. Enomoto; Relations for Grothendieck groups and representation-finiteness; Journal of Algebra
Volume 539, 1 December 2019, Pages 152-176.
Požadavky ke zkoušce -
Poslední úprava: doc. RNDr. Jan Šťovíček, Ph.D. (11.10.2017)
Předmět je zakončen ústní zkouškou. Požadavky u zkoušky budou odpovídat rozsahu, ve kterém bylo téma prezentováno na přednášce.
Poslední úprava: doc. RNDr. Jan Šťovíček, Ph.D. (11.10.2017)
The course is completed with an oral exam. The requirements for the exam correspond to what is presented in lectures.
Sylabus -
Poslední úprava: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (05.01.2024)
This course will be about Cohen-Macaulay modules over local Cohen-Macaulay rings, with a view
towards Auslander-Reiten sequences and what it means for such sequences to generate the relations of
the Grothendieck group. Depending on time and interest, we may consider these questions in the
generality of Exact categories which has applications to (Cohen-Macaulay) orders.
(1) Recalling definitions of Cohen-Macaulay rings, (maximal)Cohen-Macaulay modules, Gorenstein
rings.
(2) Exact categories.
(3) Auslander-Reiten sequences.
(4) Functor categories, and the subcategories of finitely generated, and finitely presented functors.
(5) Grothendieck groups.
(6) When are the relations in the Grothendieck group generated by Auslander-Reiten sequences?
Poslední úprava: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (05.01.2024)
This course will be about Cohen-Macaulay modules over local Cohen-Macaulay rings, with a view
towards Auslander-Reiten sequences and what it means for such sequences to generate the relations of
the Grothendieck group. Depending on time and interest, we may consider these questions in the
generality of Exact categories which has applications to (Cohen-Macaulay) orders.
(1) Recalling definitions of Cohen-Macaulay rings, (maximal)Cohen-Macaulay modules, Gorenstein
rings.
(2) Exact categories.
(3) Auslander-Reiten sequences.
(4) Functor categories, and the subcategories of finitely generated, and finitely presented functors.
(5) Grothendieck groups.
(6) When are the relations in the Grothendieck group generated by Auslander-Reiten sequences ?
