nLab change of rings theorem

Statement

Let $A$ be a Hopf algebra over a field $k$, and let $B$ be a normal sub Hopf algebra of $A$. Then

$$Cotor_A(B,k) \simeq Cotor_{A//B}(k,k) \,.$$

This is used in computations with the Adams spectral sequence.

References

Due to

• A. Liulevicius, Notes on Homotopy of Thom Spectra, Amer. J. of Math., 86 (1964), 1-16.

Textbook accounts include

• Stanley Kochman, prop. 3.7.4 of Bordism, Stable Homotopy and Adams Spectral Sequences, AMS 1996

• Doug Ravenel, theorems A1.1.18, A1.1.20 and A1.1.13 in Complex cobordism and stable homotopy groups of spheres Academic Press 1986