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The category (that is, $(\infty, 1)$-category) of derived affine schemes is the opposite category of the localization of simplicial commutative rings in weak equivalences (or, equivalently, the localization of the category of commutative dg-algebras concentrated in non-positive degrees).

See extensive category. Does this result exist in the literature?

I have difficulty transferring the usual (obvious) proof from discrete rings to simplicial ones, because the product $A \times B$ is not cofibrant. And with cofibrant replacement, idemptotents cease to be strict.

It's surprising if some work is actually needed here, because conceptually the fact should be very simple. I'm probably just missing something.

The category (that is, $(\infty, 1)$-category) of derived affine schemes is the opposite category of the localization of simplicial commutative rings in weak equivalences.

See extensive category. Does this result exist in the literature?

I have difficulty transferring the usual (obvious) proof from discrete rings to simplicial ones, because the product $A \times B$ is not cofibrant. And with cofibrant replacement, idemptotents cease to be strict.

It's surprising if some work is actually needed here, because conceptually the fact should be very simple. I'm probably just missing something.

UPD. I removed the erroneous comment about equivalence with the category of dg algebras, but in reality this result is enough for me for algebras over the field of characteristic 0 (where there is an equivalence with dg algebras), if this, of course, simplifies something.

The category (that is, $(\infty, 1)$-category) of derived affine schemes is the opposite category of the localization of simplicial commutative rings in weak equivalences (or, equivalently, the localization of the category of commutative dg-algebras concentrated in non-positive degrees).

See extensive category. Does this result exist in the literature?

I have difficulty transferring the usual (obvious) proof from discrete rings to simplicial ones, because the product $A \times B$ is not cofibrant. And with cofibrant replacement, idemptotents cease to be strict.

It's surprising if some work is actually needed here, because conceptually the fact should be very simple. I'm probably just missing something.

The category (that is, $(\infty, 1)$-category) of derived affine schemes is the opposite category of the localization of simplicial commutative rings in weak equivalences (or, equivalently, the localization of the category of commutative dg-algebras concentrated in non-positive degrees).

See extensive category. Does this result exist in the literature?

I have difficulty transferring the usual (obvious) proof from discrete rings to simplicial ones, because the product $A \times B$ is not cofibrant. And with cofibrant replacement, idemptotents cease to be strict.

It's surprising if some work is actually needed here, because conceptually the fact should be very simple. I'm probably just missing something.

The category (that is, the $(\infty, 1)$-category) of derived affine schemes is the opposite category of the localization of simplicial commutative rings in weak equivalences (or, equivalently, the localization of the category of dg-algebras concentrated in non-positive degrees).

See extensive category. Does this result exist in the literature?

I have difficulty transferring the usual (obvious) proof from discrete rings to simplicial ones (or equivalent: connected j-algebras), because the product $A \times B$ is not cofibrant. And with cofibrant replacement, idemptotents cease to be strict.

It's surprising if some work is actually needed here, because conceptually the fact should be very simple. I'm probably just missing something.

The category (that is, $(\infty, 1)$-category) of derived affine schemes is the opposite category of the localization of simplicial commutative rings in weak equivalences (or, equivalently, the localization of the category of commutative dg-algebras concentrated in non-positive degrees).

See extensive category. Does this result exist in the literature?

I have difficulty transferring the usual (obvious) proof from discrete rings to simplicial ones, because the product $A \times B$ is not cofibrant. And with cofibrant replacement, idemptotents cease to be strict.

It's surprising if some work is actually needed here, because conceptually the fact should be very simple. I'm probably just missing something.