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I was reading about cotangent complexes in derived algebraic geometry. I saw the following two surprising conjectures by Quillen (from "Cohomology of commutative rings").

My question is does these conjectures are proved? Does anything is known using derived or spectral algebraic geometry?

My question is: are these conjectures proved? Is anything known using derived or spectral algebraic geometry?

pic

I was reading about cotangent complexes in derived algebraic geometry. I saw the following two surprising conjectures by Quillen (from "Cohomology of commutative rings").

My question is does these conjectures are proved? Does anything is known using derived or spectral algebraic geometry?

pic

I was reading about cotangent complexes in derived algebraic geometry. I saw the following two surprising conjectures by Quillen (from "Cohomology of commutative rings").

My question is: are these conjectures proved? Is anything known using derived or spectral algebraic geometry?

pic

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Quillen's conjecture

I was reading about cotangent complexes in derived algebraic geometry. I saw the following two surprising conjectures by Quillen (from "Cohomology of commutative rings").

My question is does these conjectures are proved? Does anything is known using derived or spectral algebraic geometry?

pic