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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 …

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 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 …

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 …

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 …

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 …

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 …

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 …

Is there an notion of elliptic curve over the field with one element? As I learned from a previous question, there are several different versions of what the field with one element and what schemes o …

What is the "theorem of the cube" for abelian varieties? What is the statement and how should I think about it?

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 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 …

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 …

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 $ …