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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
6
votes
1
answer
701
views
descent implies hyperdescent
My question concerns the Propsition 5.12 of the paper of Bhatt-Mathew on arc-topology where they claim that the functor $X\mapsto D^b_{\text{cons}}(X,\Lambda)^{[-n,n]}$ which assigns to a qcqs scheme …
4
votes
1
answer
734
views
Infinitely many exceptional curves on ruled surfaces
Take an algebraically closed field $k$. Let $C$ be a smooth projective variety of dimension $1$ over $k$(a curve). Consider a geometrically ruled surface $S :=C\times\mathbb{P}^1$. Does there exist …
1
vote
1
answer
276
views
What does the group of automorphisms corresponding to $\mathfrak{g}$
I am reading a book titled "Lectures on An Introduction to Grothendieck's Theory of the Fundamental Group" by J.P. Murre. I am in the chapter 4 titled "Fundamental groups". Here he fixes a base locall …