Journal of K-theory: K-theory and Its Applications To Algebra, Geometry, and Topology 

About: Journal of K-theory: K-theory and Its Applications To Algebra, Geometry, and Topology is an academic journal. The journal publishes majorly in the area(s): Ring (mathematics) & K-theory. Over the lifetime, 13 publications have been published receiving 114 citations.

Recollement of homotopy categories and Cohen-Macaulay modules

Abstract: We study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. We show the existence of a recollement of the above quotient category and it has the homotopy category of acyclic complexes as a triangulated subcategory. In the case of the homotopy category of finitely gen- erated projective modules over an Iwanaga-Gorenstein ring, we show that the above quotient category are triangle equivalent to the stable module category of Cohen-Macaulay T2(R)-modules.

Towards a K-theoretic characterization of graded isomorphisms between Leavitt path algebras

Abstract: In Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs.

Compactly supported analytic indices for Lie groupoids

Abstract: For any Lie groupoid we construct an analytic index morphism taking values in a modified K theory group which involves the convolution algebra of compactly sup- ported smooth functions over the groupoid. The construction is performed by using the deformation algebra of smooth functions over the tangent groupoid constructed in (CR06). This allows in particular to prove a more primitive version of the Connes-Skandalis Lon- gitudinal index Theorem for foliations, that is, an index theorem taking values in a group which pairs with Cyclic cocycles. As other application, for D a G PDO elliptic operator with associated index indD 2 K0(C 1 (G)), we prove that the pairing , witha bounded continuous cyclic cocycle, only depends on the principal symbol class (�(D)) 2 K 0 (AG). The result is completely general forgroupoids. We discuss some potential applications to the Novikov's conjecture.

Periodicity of hermitian K -groups

Abstract: Bott periodicity for the unitary and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic Kgroups with finite coefficients, similar results are consequences of the Milnor and Bloch-Kato conjectures, affirmed by Voevodsky, Rost and others. More generally, we prove that periodicity of the algebraic K-groups for any ring implies periodicity for the hermitian K-groups, analogous to orthogonal and symplectic topological K-theory. The proofs use in an essential way higher KSC -theories, extending those of Anderson and Green. They also provide an upper bound for the higher hermitian K-groups in terms of higher algebraic K-groups. We also relate periodicity to etale hermitian K-groups by proving a hermitian version of Thomason’s etale descent theorem. The results are illustrated in detail for local fields, rings of integers in number fields, smooth complex algebraic varieties, rings of continuous functions on compact spaces, and group rings.