definition of isomorphism of ringed spaces Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)definition of morphism of ringed spacesMorphisms between locally ringed spaces and affine schemesWhen is a morphism of $k$-ringed spaces the morphism induced by pullbacks?morphism of ringed spaces glueDefinition of a morphism of locally ringed spacesGeometric intuition behind locality of morphisms of locally ringed spacesOpen vs Closed Immersions of Locally Ringed SpacesLocally ringed spaces and varietiesHow to understand $s_x_sin S$ generates $mathcal F_x$ for every $xin X$?Morphisms of Locally ringed spaces over manifolds.
Why is it faster to reheat something than it is to cook it?
GDP with Intermediate Production
Flight departed from the gate 5 min before scheduled departure time. Refund options
Proof by mathematical induction with the problem 40(2n)! ≥ 30^n
What does Turing mean by this statement?
How often does castling occur in grandmaster games?
Is there public access to the Meteor Crater in Arizona?
How can god fight other gods?
How many morphisms from 1 to 1+1 can there be?
Special flights
Moving a wrapfig vertically to encroach partially on a subsection title
Why not send Voyager 3 and 4 following up the paths taken by Voyager 1 and 2 to re-transmit signals of later as they fly away from Earth?
Why is std::move not [[nodiscard]] in C++20?
Why complex landing gears are used instead of simple,reliability and light weight muscle wire or shape memory alloys?
Why are vacuum tubes still used in amateur radios?
Is there any word for a place full of confusion?
Did pre-Columbian Americans know the spherical shape of the Earth?
What is a more techy Technical Writer job title that isn't cutesy or confusing?
Constant factor of an array
Does the Mueller report show a conspiracy between Russia and the Trump Campaign?
What adaptations would allow standard fantasy dwarves to survive in the desert?
Is multiple magic items in one inherently imbalanced?
AppleTVs create a chatty alternate WiFi network
Nose gear failure in single prop aircraft: belly landing or nose-gear up landing?
definition of isomorphism of ringed spaces
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)definition of morphism of ringed spacesMorphisms between locally ringed spaces and affine schemesWhen is a morphism of $k$-ringed spaces the morphism induced by pullbacks?morphism of ringed spaces glueDefinition of a morphism of locally ringed spacesGeometric intuition behind locality of morphisms of locally ringed spacesOpen vs Closed Immersions of Locally Ringed SpacesLocally ringed spaces and varietiesHow to understand $s_x_sin S$ generates $mathcal F_x$ for every $xin X$?Morphisms of Locally ringed spaces over manifolds.
$begingroup$
I'm reading Qing Liu's "Algebraic Geometry and Arithmetic Curves." p. 38. I'm not sure I clearly understood the definition of an isomorphism of ringed spaces. In my book, ringed space always mean locally ringed space. The following is the definition of isomorphism from the book:
An isomorphism is an invertible morphism.
So suppose we have two ringed spaces $(X,mathcal O_X)$ and $(Y,mathcal O_Y)$ and a morphism $(f,f^#):(X,mathcal O_X)to(Y,mathcal O_Y)$. To say that $(f,f^#)$ is invertible, does it mean that there is a morphism $(g,g^#):(Y,mathcal O_Y)to(X,mathcal O_X)$ such that both compositions $(f,f^#)circ(g,g^#)$ and $(g,g^#)circ(f,f^#)$ are identity morphisms?
algebraic-geometry
asked Apr 2 at 10:30
zxcvzxcv
1919
$endgroup$
add a comment |
$begingroup$
I'm reading Qing Liu's "Algebraic Geometry and Arithmetic Curves." p. 38. I'm not sure I clearly understood the definition of an isomorphism of ringed spaces. In my book, ringed space always mean locally ringed space. The following is the definition of isomorphism from the book:
An isomorphism is an invertible morphism.
So suppose we have two ringed spaces $(X,mathcal O_X)$ and $(Y,mathcal O_Y)$ and a morphism $(f,f^#):(X,mathcal O_X)to(Y,mathcal O_Y)$. To say that $(f,f^#)$ is invertible, does it mean that there is a morphism $(g,g^#):(Y,mathcal O_Y)to(X,mathcal O_X)$ such that both compositions $(f,f^#)circ(g,g^#)$ and $(g,g^#)circ(f,f^#)$ are identity morphisms?
algebraic-geometry
asked Apr 2 at 10:30
zxcvzxcv
1919
$endgroup$
$begingroup$
Yes. This definition of isomorphism is completely general.
$endgroup$
– KReiser
Apr 2 at 18:26
add a comment |
$begingroup$
I'm reading Qing Liu's "Algebraic Geometry and Arithmetic Curves." p. 38. I'm not sure I clearly understood the definition of an isomorphism of ringed spaces. In my book, ringed space always mean locally ringed space. The following is the definition of isomorphism from the book:
An isomorphism is an invertible morphism.
So suppose we have two ringed spaces $(X,mathcal O_X)$ and $(Y,mathcal O_Y)$ and a morphism $(f,f^#):(X,mathcal O_X)to(Y,mathcal O_Y)$. To say that $(f,f^#)$ is invertible, does it mean that there is a morphism $(g,g^#):(Y,mathcal O_Y)to(X,mathcal O_X)$ such that both compositions $(f,f^#)circ(g,g^#)$ and $(g,g^#)circ(f,f^#)$ are identity morphisms?
algebraic-geometry
asked Apr 2 at 10:30
zxcvzxcv
1919
$endgroup$
I'm reading Qing Liu's "Algebraic Geometry and Arithmetic Curves." p. 38. I'm not sure I clearly understood the definition of an isomorphism of ringed spaces. In my book, ringed space always mean locally ringed space. The following is the definition of isomorphism from the book:
An isomorphism is an invertible morphism.
So suppose we have two ringed spaces $(X,mathcal O_X)$ and $(Y,mathcal O_Y)$ and a morphism $(f,f^#):(X,mathcal O_X)to(Y,mathcal O_Y)$. To say that $(f,f^#)$ is invertible, does it mean that there is a morphism $(g,g^#):(Y,mathcal O_Y)to(X,mathcal O_X)$ such that both compositions $(f,f^#)circ(g,g^#)$ and $(g,g^#)circ(f,f^#)$ are identity morphisms?
algebraic-geometry
algebraic-geometry
asked Apr 2 at 10:30
zxcvzxcv
1919
asked Apr 2 at 10:30
zxcvzxcv
1919
asked Apr 2 at 10:30
zxcvzxcv
1919
asked Apr 2 at 10:30
zxcvzxcv
1919
asked Apr 2 at 10:30
zxcvzxcv
1919
1919
$begingroup$
Yes. This definition of isomorphism is completely general.
$endgroup$
– KReiser
Apr 2 at 18:26
add a comment |
$begingroup$
Yes. This definition of isomorphism is completely general.
$endgroup$
– KReiser
Apr 2 at 18:26
$begingroup$
Yes. This definition of isomorphism is completely general.
$endgroup$
– KReiser
Apr 2 at 18:26
$begingroup$
Yes. This definition of isomorphism is completely general.
$endgroup$
– KReiser
Apr 2 at 18:26
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3171697%2fdefinition-of-isomorphism-of-ringed-spaces%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3171697%2fdefinition-of-isomorphism-of-ringed-spaces%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Yes. This definition of isomorphism is completely general.
$endgroup$
– KReiser
Apr 2 at 18:26