What is “locally integral” in Mumford's GIT book? The 2019 Stack Overflow Developer Survey Results Are Inbasic question on integral schemesProperties preserved by categorical quotient (after Mumford's GIT)basic question on integral schemesWhat are normal schemes intuitively?True/False about ring and integral domainThe local ring of the generic point of a prime divisorEvery commutative ring is a quotient of a normal ring?Suppose that $f/g$ is a rational function on an integral scheme $X$, which we know to be locally regular. Then is $f/g$ regular?A characterization of normal schemes (clarification of a statement of proposition)example of a normal proper flat scheme over $mathbbZ$?Universal Property of Integral ClosureConfusion on the definition of “locally of finite presentation”
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What is “locally integral” in Mumford's GIT book?
The 2019 Stack Overflow Developer Survey Results Are Inbasic question on integral schemesProperties preserved by categorical quotient (after Mumford's GIT)basic question on integral schemesWhat are normal schemes intuitively?True/False about ring and integral domainThe local ring of the generic point of a prime divisorEvery commutative ring is a quotient of a normal ring?Suppose that $f/g$ is a rational function on an integral scheme $X$, which we know to be locally regular. Then is $f/g$ regular?A characterization of normal schemes (clarification of a statement of proposition)example of a normal proper flat scheme over $mathbbZ$?Universal Property of Integral ClosureConfusion on the definition of “locally of finite presentation”
$begingroup$
I think "locally integral" means for each point of a scheme, its local ring is a domain. In my definition, "normal" obviously implies "locally integral". But "normal" and "locally integral" is mentioned independently in Mumford's GIT book, as the image below.
What is definition of "locally integral"? And if my definition of it is correct, how can I prove that "locally integral" is preserved by taking a categorical quotient?
abstract-algebra algebraic-geometry geometric-invariant-theory
asked Mar 13 at 10:49
LOCOASLOCOAS
456
$endgroup$
add a comment |
$begingroup$
I think "locally integral" means for each point of a scheme, its local ring is a domain. In my definition, "normal" obviously implies "locally integral". But "normal" and "locally integral" is mentioned independently in Mumford's GIT book, as the image below.
What is definition of "locally integral"? And if my definition of it is correct, how can I prove that "locally integral" is preserved by taking a categorical quotient?
abstract-algebra algebraic-geometry geometric-invariant-theory
asked Mar 13 at 10:49
LOCOASLOCOAS
456
$endgroup$
add a comment |
$begingroup$
I think "locally integral" means for each point of a scheme, its local ring is a domain. In my definition, "normal" obviously implies "locally integral". But "normal" and "locally integral" is mentioned independently in Mumford's GIT book, as the image below.
What is definition of "locally integral"? And if my definition of it is correct, how can I prove that "locally integral" is preserved by taking a categorical quotient?
abstract-algebra algebraic-geometry geometric-invariant-theory
asked Mar 13 at 10:49
LOCOASLOCOAS
456
$endgroup$
I think "locally integral" means for each point of a scheme, its local ring is a domain. In my definition, "normal" obviously implies "locally integral". But "normal" and "locally integral" is mentioned independently in Mumford's GIT book, as the image below.
What is definition of "locally integral"? And if my definition of it is correct, how can I prove that "locally integral" is preserved by taking a categorical quotient?
abstract-algebra algebraic-geometry geometric-invariant-theory
abstract-algebra algebraic-geometry geometric-invariant-theory
asked Mar 13 at 10:49
LOCOASLOCOAS
456
asked Mar 13 at 10:49
LOCOASLOCOAS
456
asked Mar 13 at 10:49
LOCOASLOCOAS
456
asked Mar 13 at 10:49
LOCOASLOCOAS
456
asked Mar 13 at 10:49
LOCOASLOCOAS
456
456
add a comment |
add a comment |
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