Monadic resolutions for (generalized) spaces

Vom41941 — Fri, 01 May 2026 08:00:22 GMT

Created page with "Understanding the homotopy type of a space often benefits from studying its values under homology theories. Every homology theory determines a Bousfield localization on the category of spaces — for example, rational cohomology leads to rationalization, while $F_p$-homology induces $p$-completion. In favorable cases, these localizations admit explicit descriptions via monadic resolutions. A key example is the $p$-completion $L_p X$ of a nilpotent space $X$, which can..."

New page

Understanding the homotopy type of a space often benefits from studying its values under homology theories. Every homology theory determines a Bousfield localization on the category of spaces — for example, rational cohomology leads to rationalization, while $F_p$-homology induces $p$-completion.
In favorable cases, these localizations admit explicit descriptions via monadic resolutions.
A key example is the $p$-completion $L_p X$ of a nilpotent space $X$, which can be expressed as an inverse limit:
$L_p X = lim_n (\Omega^\infty F_p \otimes \Sigma^\infty)^{n+1}(X)$.
Similarly, any nilpotent space $X$ can be expressed as the inverse limit
$X = lim_n (\Omega^\infty MU \otimes \Sigma^\infty)^{n+1}(X)$ of its iterated $MU$-homology, giving rise to the unstable Adams—Novikov spectral sequence.
A fundamental ingredient in proving this equivalence is Bousfield and Kan's celebrated principal fibration lemma.

In this talk, I will discuss how these ideas extend to oo-topoi and explain their application in motivic homotopy theory. In particular, I will sketch a proof of the principal fibration lemma in this broader context.
This is joint work with Tom Bachmann and Anton Engelmann.

AG-Seminar WS2021/22:

Vom41941 — Fri, 01 May 2026 07:59:08 GMT

← Older revision		Revision as of 09:59, 1 May 2026
(One intermediate revision by the same user not shown)
Line 34:		Line 34:
	\|4		\|4
	\|7.5.2026		\|7.5.2026
	\| ~~TBA~~		\| [[Monadic resolutions for (generalized) spaces]]
	\| Klaus Mattis (Mainz)		\| Klaus Mattis (Mainz)
	\|-		\|-
Line 79:		Line 79:
	\|13		\|13
	\|9.7.2026		\|9.7.2026
	\|		\| TBA
	\|		\| Leor Neuhauser (Hebrew University of Jerusalem)
	\|-		\|-
	\|14		\|14

SFB1085 - Higher Invariants - Recent changes [en]

Monadic resolutions for (generalized) spaces

AG-Seminar WS2021/22: