Serre sequences and Chern classes

Classes of Modules Related to Serre Subcategories

Let R be an associative ring with non-zero identity. For a Serre subcategory C of the category R-mod of left R-modules, we consider the class AC of all modules that do not belong to C, but all of their proper submodules belong to C. Alongside of basic properties of such associated classes of modules, we will prove that every uniform module of AC has a local endomorphism ring. Moreover, if R is ...

Chow Homology and Chern Classes

Stringy Chern classes

Work of Dixon, Harvey, Vafa and Witten in the 80’s ([DHVW85]) introduced a notion of Euler characteristic (for quotients of a torus by a finite group) which became known as the physicist’s orbifold Euler number. In the 90’s V. Batyrev introduced a notion of stringy Euler number ([Bat99b]) for ‘arbitrary Kawamata log-terminal pairs’, proving that this number agrees with the physicist’s orbifold ...

Spectral Sequences for Noncommutative Serre Fibrations

We prove in this paper a noncommutative version of Leray Theorem and then Leray-Serre Spectral Theorem for noncommutative Serre fibrations: for NC Serre fibration there are converging spectral sequences with E2 terms as E2 p,q = HPp(A;HPq(B,A)) =⇒ HPp+q(B) and E 2 p,q = HPp(A;Kq(B,A)) =⇒ Kp+q(B). Introduction The ideas of using spectral sequences to operator algebras was started in [C]. In that...

Spectral Sequences for Noncommutive Serre Fibrations

We prove in this paper a noncommutative version of Leray Theorem and then Serre Spectral Theorem for noncommutative Serre fibrations. We prove that for NC Serre fibration there are converging spectral sequences with E2 terms as E2 p,q = HPp(B,A;HPq(A)) =⇒ HPp+q(B) and E 2 p,q = HPp(B,A;Kq(A)) =⇒ Kp+q(B). Introduction The ideas of using spectral sequences to operator algebras was started in [C]....