Homology Comodules

Injective Comodules and Landweber Exact Homology Theories

We classify the indecomposable injective E(n)∗E(n)-comodules, where E(n) is the Johnson-Wilson homology theory. They are suspensions of the Jn,r = E(n)∗(MrE(r)) where 0 ≤ r ≤ n, with the endomorphism ring of Jn,r being Ê(r) ∗ Ê(r), where Ê(r) denotes the completion of E(r).

CYCLIC COMODULES, THE HOMOLOGY OF j, AND j-HOMOLOGY

This short paper arose as a warm-up to the more difficult computations at the primes 2 and 3 of connective versions of Behrens’ Q(2) spectrum, a spectrum conjecturally describing half of the K(2)-local sphere [2]. The natural starting case is to understand the K(1)-local story, giving rise to the present discussion of the homology of the connective image of J spectrum. The homology results are ...

On Corings and Comodules

It is shown that the categories of R-coalgebras for a commutative unital ring R and the category of A-corings for some R-algebra A as well as their respective categories of comodules are locally presentable.

Model theory of comodules

Flat Connections and Comodules

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...