From a48d2c2ee6084d331c8456020f8e5f272a2f502f Mon Sep 17 00:00:00 2001 From: Felix Cherubini Date: Mon, 4 Mar 2024 22:18:44 +0100 Subject: [PATCH] Write the conclusion of #18 to the answered questions part of the README --- README.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/README.md b/README.md index f5d9f03..c092613 100644 --- a/README.md +++ b/README.md @@ -39,6 +39,9 @@ There is a related [formalization project](https://github.com/felixwellen/synthe - Is $\mathrm{Spec} A$ quasi-complete ("compact") for $A$ a finite $R$-algebra (fin gen as $R$-module)? *Yes*: By the discussion in [#5](../../issues/5) and [#6](../../issues/6), $\mathrm{Spec} A$ is even projective, whenever $A$ is finitely generated as an $R$-module. +- Can there be a flat-modality for $\mathbb{A}^1$-homotopy theory? + + *No*: By the disucssion in [#18](../../issues/18), this should not be possible, because it would imply that the category of $\mathbb{A}^1$-local types is a topos, which is known to be false. # Learning material There are some [recordings](https://www.youtube.com/playlist?list=PLrnCInSNK7UT_JnKwnderE8eIkWtoW_az) of talks from the last [workshop](https://www.felix-cherubini.de/sag-meeting-3.html) on synthetic algebraic geometry.