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The K3 manifold is an amazing object in mathematics which plays an important role in several fields ranging from the study of smooth 4-manifolds to algebraic geometry to differential geometry and beyo …

Yes, there is something to this effect. In fact there is a very general context for this. Since I know you are amenable to $\infty$-categories, I will use that language. The homotopy theory of spa …

I am an algebraic topologist and am trying to understand some computations related to p-adic complex K-theory and equivariant K-theory. However this has led me into the world of algebraic geometry ove …

As per Todd's suggestion I am posting this as an answer. The $(\infty, n)$-category of bordisms is an important example for many reasons, the most imporant of which is its role in the Baez-Dolan cob …

This is not true. It fails for essentially the same reason that the category of topological commutative groups fail to be an abelian category. For simplicity let's work over an algebraically closed …

So thanks to the comments of Tyler Lawson I have been able to figure out what is happening in this example, so I thought I should post it as an answer. I think this is also what Torsten Ekedahl was ge …

I think I am confused about some terminology in algebraic geometry, specifically the meaning of the term "torsor". Suppose that I fix a scheme S. I want to work with torsors over S. Let $\mu$ be a she …

I want to know exactly how derived functor cohomology and Cech cohomology can fail to be the same. I started worrying about this from Dinakar Muthiah's answer to an MO question, and Brian Conrad's com …

I have a couple things to say. First, believe your definition of gerbe is slightly incorrect. When you say that your stack is locally isomorphic to $U \times B\mathbb{G}_m$, this isomorphism needs to …

My recollection is that when you turn these into analytic spaces you get something which is locally contractible topologically. In this case what you are describing is a principal bundle for locally c …

This issue or question came up indirectly in a couple previous posts, which I think you might like to look at. There is indeed a notion of algebraic space which is more general and doesn't require qua …

Maybe I am miss understanding the question, but it seems the answer is yes. Take your favorite G-space, mine is $S^1$ with the $\mathbb{Z}/2$-action "flip". Then consider the trivial vector bundles $ …

A scheme is separated if the diagonal inclusion $X \to X \times X$ is a closed immersion. I what to know if there is a good generalization of `separated' for algebraic stacks? My usual stack referenc …

Let me say first that I am not an algebraic geometer. Nevertheless, in trying to understand the answers to this very question I asked the following question. After hearing the ensuing answers it seems …

This question is related to the question Is an algebraic space group always a scheme? which I've just seen which was posted by Anton. His question is whether an algebraic space which is a group object …