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In The Geometry of Schemes by David Eisenbud and Joe Harris, on page 57, there is an explanation on "node" of a plane curve. The book says that, a curve $X\subseteq \mathbb A_{\mathbb C}^2$ ...

I have a few naive questions on the algebraic K-theory spectrum construction, but whose answers I couldn't figure out using the internet. I'm mostly interested in the case of a commutative ring, but I ...

Nowadays there is a lot of talk about derived algebraic geometry, but not so much about the related subject of spectral algebraic geometry. Now I'm curious what future is there for spectral algebraic ...

It is my dream to do research on applications of spectral algebraic geometry in homotopy theory one day. Specifically, giving a more uniform treatment for the results proved via scary computations (of ...

So I've been trying to learn some derived algebraic geometry, and I've chosen to approach the subject from the perspective of spectral or "brave new" algebraic geometry. Without having to go through ...

Theorem 4.5.4.7 (4.4.4.7 in the old version) in Lurie's Higher Algebra (or Theorem 4.3.22 in DAG III) states (roughly speaking) that under certain conditions the ∞-category of commutative ∞-monoids in ...