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Hsuan-Yi Liao
Hsuan-Yi Liao
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I'm looking for a theorem about quotient of quasi-isomorphic cdga's:

Let $A, B$ be two cdga's (commutative differential graded$\mathbb Z$-graded algebra) of nonpositive degrees, and $\mathfrak m \subset A, \mathfrak n \subset B$ be maximal ideals closed under differentials. Suppose $\phi: A \to B$ is a quasi-isomorphism of cdga's and $\phi(\mathfrak m) \subset \mathfrak n$. Is the induced map $\phi: A/ \mathfrak m^2 \to B/\mathfrak n^2$ still a quasi-isomorphism?

I guess more assumptions on $A,B, \mathfrak m, \mathfrak n$ might be needed. Any theorems of this type would be helpful.

I'm looking for a theorem about quotient of quasi-isomorphic cdga's:

Let $A, B$ be two cdga's (commutative differential graded algebra) of nonpositive degrees, and $\mathfrak m \subset A, \mathfrak n \subset B$ be maximal ideals closed under differentials. Suppose $\phi: A \to B$ is a quasi-isomorphism of cdga's and $\phi(\mathfrak m) \subset \mathfrak n$. Is the induced map $\phi: A/ \mathfrak m^2 \to B/\mathfrak n^2$ still a quasi-isomorphism?

I guess more assumptions on $A,B, \mathfrak m, \mathfrak n$ might be needed. Any theorems of this type would be helpful.

I'm looking for a theorem about quotient of quasi-isomorphic cdga's:

Let $A, B$ be two cdga's (commutative differential $\mathbb Z$-graded algebra) of nonpositive degrees, and $\mathfrak m \subset A, \mathfrak n \subset B$ be maximal ideals closed under differentials. Suppose $\phi: A \to B$ is a quasi-isomorphism of cdga's and $\phi(\mathfrak m) \subset \mathfrak n$. Is the induced map $\phi: A/ \mathfrak m^2 \to B/\mathfrak n^2$ still a quasi-isomorphism?

I guess more assumptions on $A,B, \mathfrak m, \mathfrak n$ might be needed. Any theorems of this type would be helpful.

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Source Link
Hsuan-Yi Liao
Hsuan-Yi Liao
  • 151
  • 2

I'm looking for a theorem about quotient of quasi-isomorphic cdga's:

Let $A, B$ be two cdga's (commutative differential graded algebra) of nonpositive degrees, and $\mathfrak m \subset A, \mathfrak n \subset B$ be maximal ideals closed under differentials. Suppose $\phi: A \to B$ is a quasi-isomorphism of cdga's and $\phi(\mathfrak m) \subset \mathfrak n$. Is the induced map $\phi: A/ \mathfrak m \to B/\mathfrak n$$\phi: A/ \mathfrak m^2 \to B/\mathfrak n^2$ still a quasi-isomorphism?

I guess more assumptions on $A,B, \mathfrak m, \mathfrak n$ might be needed. Any theorems of this type would be helpful.

I'm looking for a theorem about quotient of quasi-isomorphic cdga's:

Let $A, B$ be two cdga's (commutative differential graded algebra), and $\mathfrak m \subset A, \mathfrak n \subset B$ be maximal ideals. Suppose $\phi: A \to B$ is a quasi-isomorphism of cdga's and $\phi(\mathfrak m) \subset \mathfrak n$. Is the induced map $\phi: A/ \mathfrak m \to B/\mathfrak n$ still a quasi-isomorphism?

I guess more assumptions on $A,B, \mathfrak m, \mathfrak n$ might be needed. Any theorems of this type would be helpful.

I'm looking for a theorem about quotient of quasi-isomorphic cdga's:

Let $A, B$ be two cdga's (commutative differential graded algebra) of nonpositive degrees, and $\mathfrak m \subset A, \mathfrak n \subset B$ be maximal ideals closed under differentials. Suppose $\phi: A \to B$ is a quasi-isomorphism of cdga's and $\phi(\mathfrak m) \subset \mathfrak n$. Is the induced map $\phi: A/ \mathfrak m^2 \to B/\mathfrak n^2$ still a quasi-isomorphism?

I guess more assumptions on $A,B, \mathfrak m, \mathfrak n$ might be needed. Any theorems of this type would be helpful.

Source Link
Hsuan-Yi Liao
Hsuan-Yi Liao
  • 151
  • 2

Quotient of quasi-isomorphic cdga's

I'm looking for a theorem about quotient of quasi-isomorphic cdga's:

Let $A, B$ be two cdga's (commutative differential graded algebra), and $\mathfrak m \subset A, \mathfrak n \subset B$ be maximal ideals. Suppose $\phi: A \to B$ is a quasi-isomorphism of cdga's and $\phi(\mathfrak m) \subset \mathfrak n$. Is the induced map $\phi: A/ \mathfrak m \to B/\mathfrak n$ still a quasi-isomorphism?

I guess more assumptions on $A,B, \mathfrak m, \mathfrak n$ might be needed. Any theorems of this type would be helpful.