Search Results

I don't think that $\bar\alpha$ is always the identity. You should think of $\alpha$ as a ``path'' from $x$ to $y$, so in principle it is possible that the loop obtained as the image of $\alpha$ is no …

As Harry Gindy as said in the comments, there is a refinement of the notion of shape due to Barwick, Glasman and Haine that contains much more information that just the shape. This is not a pro-space, …

Let $X$ be a quasi-compact and quasi-separated scheme, and $U\subseteq X$ be a quasi-compact open subscheme. Then we can consider $Rj_*\mathcal{O}_U$ the (derived) pushforward of the structure sheaf o …

This question is strongly related to this question. However it seems to me sufficiently distinct to warrant asking it separately. Let $X$ be a quasi-compact, quasi-separated scheme. When is the ∞- …

I think that the same proof that it is usually done for torsors will work for these "Hopf-torsors", at least when $H$ is of finite presentation over the base. Maybe you are able to remove that hypothe …

In general the statement is slightly different. What you typically have is a presheaf $F$ of groupoids (i.e. for every element $X$ you can have $QCoh(X)$ the groupoid of quasicoherent sheaves and isom …

Another reference is Tag 01KO in the Stacks project (note that when $S$ is affine the hypothesis that the two opens map into a common affine is empty). Of course, the condition that the intersection …

No, homotopy classes of maps of unpointed spaces are not equivalent to homotopy classes of maps of pointed spaces. You need to be a little bit more clever. What follows is a spelling out of Brown's or …

No, the definition in Schlichting's first paper are not the "correct" definition of higher Witt groups (in any case they are not the analogue of Balmer's Witt groups), rather they are some shifted hig …

The étale topos of a field $k$ is just the topos of sets with a continuous $\mathrm{Gal}(k)$-action (here continuous is equivalent to all stabilizers being open), hence it is the colimit (in the ∞-cat …

This is the first time I ask a question on Mathoverflow, so I apologize in advance if it is not suitable/a duplicate/otherwise inappropriated. I am thinking about Voevodsky's category of motives and …

These are really two questions but I hope that the same method will solve both of them. For the purpose of this question let us fix a real closed field $R$, a bounded semialgebraic set $X$ over $R$, …

Is there a notion of smoothness for maps of real closed spaces in the sense of Schwartz? [1] Ideally it would have the following properties: Every smooth map of real closed spaces is locally of the …

I've decided to expand my comment into an answer. The point is what do you think a topology is for. If you think that a topology is for talking about convergence of sequences, then no the Zariski top …

What is true is that there is an antiequivalence between the category of schemes affine over $S$ (that is $S$-schemes for which the preimage of an open affine of $S$ is an open affine) and quasi-coher …