Timeline for Spin structure for varieties, especially finite field

6 events

when toggle format	what		by	license	comment
Sep 10, 2018 at 17:46	vote	accept	Simon Lentner
Jun 20, 2016 at 22:29	history	edited	Qiaochu Yuan	CC BY-SA 3.0	added 2242 characters in body
Jun 20, 2016 at 22:03	comment	added	Branimir Ćaćić		Ah, OK, that makes sense. And even in the $\mathbb{C}$-algebra case, given that $\mathbb{CP}^{2k}$ is spin$^\mathbb{C}$ but not spin, I suppose you'd might as well work with something more precisely akin to spin$^\mathbb{C}$?
Jun 20, 2016 at 21:55	comment	added	Qiaochu Yuan		@Branimir: I guess it depends on whether you have in mind the case that $k$ is a $\mathbb{C}$-algebra or an $\mathbb{R}$-algebra.
Jun 20, 2016 at 21:47	comment	added	Branimir Ćaćić		Unless I'm missing something, what you're describing is more like a spin$^\mathbb{C}$ structure, no? Following Plymen, to get something like a spin structure, you'd presumably need $M$ isomorphic to $\operatorname{Hom}_k(M,k)$ as $\operatorname{Cl}(V,q)$-modules, where $\operatorname{Hom}_k(M,k)$ is given the $\operatorname{Cl}(V,q)$-module structure induced by the order-reversing anti-automorphism on $\operatorname{Cl}(V,q)$.
Jun 20, 2016 at 20:18	history	answered	Qiaochu Yuan	CC BY-SA 3.0