In this short note, we show that a group acting geometrically on CAT(0) cube complex with virtually abelian hyperplane-stabilisers must decompose as free product of groups and surface groups.

This is the text of a talk given at the Isaac Newton Institute in Cambridge on 4th August, 2006. This talk is motivated by a recent paper [A Kaygun and M Khalkhali, Hopf modules and noncommutative differential geometry, Lett. Math. Phys. 76 (2006), 77–91] in which Hopf modules appearing as coefficients in Hopf-cyclic cohomology are interpreted as modules with flat connections. We start by descr...

We study the passage from Drinfeld-A-modules to Drinfeld-A-modules for a given finite flat inclusion A ⊂ A. We show that this defines a morphism from the moduli space of Drinfeld-A-modules to the moduli space of Drinfeld-A-modules which is proper but in general not representable. For Drinfeld-Anderson shtuka and abelian sheaves instead of Drinfeld modules we obtain the same results. Mathematics...

All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. ...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.