In this article, we investigate a pair of surjective local ring maps and their relation to the canonical projection , where , are Tor-independent over R. Our main result asserts a structural connection between the homotopy Lie algebra of , denoted , in terms of those of R, , and ; namely, is the pullback of (adjusted) Lie algebras along the maps in various cases, including when the maps above have residual characteristic zero. Consequences to the main theorem include structural results on André–Quillen cohomology, stable cohomology, and Tor algebras, as well as an equality relating the Poincaré series of the common residue field of R, , , and S.
Illinois J. Math.
67(2):
383-407
(June 2023).
DOI: 10.1215/00192082-10592402
ACCESS THE FULL ARTICLE
It is not available for individual sale.
This article is only available to subscribers.
It is not available for individual sale.
It is not available for individual sale.