Titles and Short Summaries of the Talks

16 Algebra
31 Takuma Aihara (Bielefeld Univ.)
Tokuji Araya (Tokuyama Coll. of Tech.)
Osamu Iyama (Nagoya Univ.)
Ryo Takahashi (Nagoya Univ.)
Michio Yoshiwaki (Osaka City Univ.)
Final: 2013/2/7
Dimensions of triangulated categories with respect to subcategories 2
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: This talk introduces the concept of the dimension of a triangulated category with
respect to a fixed full subcategory. For the bounded derived category of an abelian category,
upper bounds of the dimension with respect to a contravariantly finite subcategory and a resolving
subcategory are given. Our methods not only recover some known results on the dimensions
of derived categories in the sense of Rouquier, but also apply to various commutative and non-
commutative noetherian rings.
32 Ryo Kanda (Nagoya Univ.) Classifying Serre subcategories via atom spectrum · · · · · · · · · · · · · · · · · 10
Summary: We introduce a spectrum of an abelian category, which we call the atom spectrum. It
is a topological space consisting of all the equivalence classes of monoform objects. In terms of the
atom spectrum, we give a classification of Serre subcategories of an arbitrary noetherian abelian
category. In the case of the module category over a commutative ring, we show that the atom
spectrum coincides with the prime spectrum of the commutative ring. As a special case of our
theorem, we recover Gabriel’s classification theorem of subcategories.
33 Hirotaka Koga (Univ. of Tsukuba) ♯ Derived equivalences and Gorenstein dimension · · · · · · · · · · · · · · · · · · · · 20
Summary: For derived equivalent left and right coherent rings we will show that the triangulated
categories of complexes of finite Gorenstein dimension are equivalent.