00:26:43 Anneloes: (Very silly question: Shouldn't "smooth schemes" be "smooth and quasi-projective schemes" here? I think algebraic cobordism is defined on a category of smooth and quasi-projective schemes so that all morphisms that you need to pull-back are lci. )
00:46:18 Fangzhou Jin: smooth schemes over k are always discrete, isn't it?
00:48:11 Federico Binda: if k is discrete, yes
00:48:33 Federico Binda: so yes if k is a field. I missed that she was working in that category for the definition
00:49:01 Federico Binda: But I thought that the category was bigger, like quasi-smooth schemes over k
00:49:31 Fangzhou Jin: Right.
00:49:36 Tom Bachmann: no
00:49:59 Federico Binda: Marc, what was the question?
00:50:22 Tom Bachmann: e.g. take Spec(k[epsilon]) -> Spec(k) iirc. This has perfect cotangent complex but in the wrong degrees.
00:50:45 Marc Noel Levine: if L_{X/Y} is perfect for X->Y map of schemes, is X->Y lci?
00:51:06 Federico Binda: No
00:51:11 Marc Noel Levine: thanks!
00:52:58 Federico Binda: In general, f\colon A \to B map of SCrng that has perfect cotangent complex is only (homotopically) of finite presentation (maybe you also need that the map on \pi_0 is classically of finite presentation, I don’t remember)
00:55:41 Tom Bachmann: smooth = flat + ..., where flat means that nothing happens on higher homotopy as discussed earlier
00:55:48 Tom Bachmann: (... what federico is saying)
01:05:24 Federico Binda: Sorry, I need to go today. See you next week!
01:19:30 Fangzhou Jin: this formula for sncd's seems to be related to resolution of singularities, is this the reason why we need it?
01:22:18 P S: from one perspective, it just tells you that the first Chern class of the line bundle of an sncd divisor is calculated via the formal group law. that explains how you define the fundamental class of sncd.
01:30:11 Marc Noel Levine: that’s right. And no need for resolution of singularities, you just need the fgl.