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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 …
Grobber's user avatar
  • 215
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 …
Grobber's user avatar
  • 215
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 …
Grobber's user avatar
  • 215