Grigory Garkusha

CLASSIFYING SERRE SUBCATEGORIES OF FINITELY PRESENTED MODULES

Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes D per (R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of isomorphism classes of indecomposable injective modules are used in an essential way.

FP-Injective and Weakly Quasi-Frobenius Rings

The classes of FP-injective and weakly quasi-Frobenius rings are investigated. The properties of both classes of rings are closely related to the embedding of finitely presented modules in fp-flat and free modules, respectively. Using these properties, we characterize the classes of coherent CF- and FGF-rings. Moreover, it is proved that the group ring R(G) is FP-injective (weakly quasi-Frobenius, respectively) if and only if the ring R is FP-injective (weakly quasi-Frobenius) and G is locally finite. Bibliography: 15 titles.

Torsion classes of finite type and spectra

Given a commutative ring

On the motivic spectral sequence

R

Classifying finite localizations of quasicoherent sheaves

(respectively a positively graded commutative ring

INJECTIVE OBJECTS IN TRIANGULATED CATEGORIES

A=\ps_{j\geq 0}A_j

Relative Homological Algebra for the Proper Class ωf

which is finitely generated as an

Algebraic Kasparov K-theory, II

A_0

R-SUPPORTS IN TENSOR TRIANGULATED CATEGORIES

-algebra), a bijection between the torsion classes of finite type in

ON THE HOMOTOPY COFIBRE SPECTRUM OF K(R) → G(R)

\Rfp