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For questions about ring spectra (in homotopy theory).

8 votes
0 answers
439 views

Descent vs effective descent for morphisms of ring spectra

Define a homomorphism $\varphi : A \to B$ of commutative discrete rings or commutative ring spectra to be a (effective) descent morphism if the comparison functor from $\mathsf{Mod}_A$ to the category …
Brendan Murphy's user avatar
2 votes
0 answers
114 views

Quasicompact quasiaffine classical schemes are nonconnectively-affine

In this answer to What is the relationship between connective and nonconnective derived algebraic geometry? I learned that any quasicompact open subscheme of an affine scheme is affine in the sense of …
Brendan Murphy's user avatar
5 votes
1 answer
328 views

Morita equivalence and connectivity

Let $A, B$ be Morita equivalent $\mathbb{E}_1$-ring spectra. Fix an an $(A, B)$-bimodule $P$ and a $(B, A)$-bimodule $Q$ such that $P \otimes_B Q \cong A$ and $Q \otimes_A P \cong B$. If $A$ is bounde …
Brendan Murphy's user avatar