Recollements and Singularity Categories
نویسندگان
چکیده
This is a report on my ongoing joint work with Martin Kalck. The recollement generated by a projective module is described. Application to singularity categories is discussed.
منابع مشابه
Highest Weight Categories and Recollements
We provide several equivalent descriptions of a highest weight category using recollements of abelian categories. Also, we explain the connection between sequences of standard and exceptional objects.
متن کاملRecollements of (derived) module categories
Recollements of abelian, resp. triangulated, categories are exact sequences of abelian, resp. triangulated, categories where the inclusion functor as well as the quotient functor have left and right adjoints. They appear quite naturally in various settings and are omnipresent in representation theory. Recollements which all categories involved are module categories (abelian case) or derived cat...
متن کاملRecollements of derived categories III: finitistic dimensions
In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely related to a longstanding conjecture, the finitistic dimension conjecture, in representation theory and homological algebra. Further, we apply our results to a ser...
متن کاملA ug 2 00 7 REFLECTING RECOLLEMENTS
A recollement describes one triangulated category T as “glued together” from two others, S and U. The definition is not symmetrical in S and U, but this note shows how S and U can be interchanged when T has a Serre functor. A recollement of triangulated categories S, T, U is a diagram of triangulated functors S i∗ // T j∗ // i ||
متن کاملRecollements of Derived Functor Categories ∗ †
We give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [H. Krause, Approximations and adjoints in homotopy categories, Math. Ann. 353 (2012), 765–781]. Then we provide a criterion for the existence of r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013