ag.algebraic geometry – formal group as the boundary of its finite subgroups

I read Manin's article on formal groups and have a problem with Lemma 1.1.
Consider $ k $ a perfect characteristic ring $ p $ and $ (A, m, k) $ a noetherian complete local ring of the same property, so that $ X = operatorname {spf} A $ is a formal group. Manin wants to prove it $ X $ is a direct limit to finite group schemas $ k $,

Define $ m ^ {(p ^ n)} $ as the ideal of
$$ {x ^ {p ^ n} | x in m }. $$
(Manin uses the notation $ m ^ {p ^ n} $ but I do not understand why $ m ^ {p ^ n} $ is generated by these elements.) He proves that $ frac {A} {m ^ {(p ^ n)}} $ are Hopf algebras and because $ A $ is completely what we have $ A = varprojlim frac {A} {m ^ {(p ^ n)}} $ as rings.

I do not understand if $ m ^ {(p ^ n)} $ is really the same $ m ^ {p ^ n} $ and if not, why? $ A $ and $ varprojlim frac {A} {m ^ {(p ^ n)}} $ can be identified as topological rings?

Sharepoint Internal names of the person or group column are changed when the list template is added

I have created a person or group column in the list. If I take a list template and use it on another site, the internal name of the person or group column is changed. I have used the internal names of this column in my code. Because of this internal name mismatch, the code fails.

amazon ec2 – Are there any disadvantages in shutting down EC2 instances of an auto-scaling group?

I want EC2 instances to shut down automatically after 24 hours.

I do that with a script that runs when the instance starts:

shutdown | at now + 24 hours

The instance shuts down and the EBS volumes stop when the instance exits.

In the console, the instance is displayed as unavailable for some time until it is declared as finished. I wonder if it is a bad practice to shut down an instance this way and if it would be better to end it with AWS CLI.

The documents say:

When an EC2 instance terminates with the terminate-instance command, the following is registered at the operating system level:

  • The API request sends an event to press a button to the guest.

  • Various system services are stopped due to the "keystroke" event. systemd shuts down the system properly. Graceful shutdown
    This is triggered by the ACPI Shutdown Button Press Event of
    Hypervisor.

  • Shutdown of ACPI is initiated.
  • The instance shuts down when the graceful shutdown completes. There is no
    configurable time to shut down the operating system.

The instance resides in an auto-scaling group that is running a REST web service. Therefore, only requests are likely to be executed.

  • What happens to requests that are still running? (The REST service has a timeout of 30 seconds, so requests no longer run.)
  • Is a cancellation with shutdown less neat than with the AWS-CLI or a termination by the auto-scaling group?

Group Theory – Odd Extensions of PSL (2, q)

Here are several questions about extensions of the group G = PSL (2, q) to Z / 2 or Z / 4 answered. But what I want to know is that there are non-trivial extensions of PSL (2, q) around an odd order group. Since the center of G is trivial, there should be no central extensions and no nontrivial maps from the odd order group to the G automorphism group. I am really only concerned with q an odd power of an odd prime number.

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Ag.algebraic geometry – Steinberg relations for elementary subgroup of a Chevalley group over an arbitrary ring

Given a semi-simple Lie algebra $ frak {g} $ of the type $ Phi $ with a Lie algebra representation $ rho: frak {g} to frak {gl} (v) $ and any commutative ring can be assigned the following gadgets:

  • A simply connected split-reduction group scheme $ G ( Phi) $ about $ R $,

  • An abstract group $ G ( Phi, R) $ which is that $ R $Points of the reducing group scheme $ G ( Phi) $ That comes up with an action $ V otimes_ mathbb {Z} R $ (Where $ V $ is a reasonable one $ mathbb {Z} $ Grid inside of $ frak {v} $ according to a Chevalley basis).

  • An abstract subgroup $ E ( Phi, R) leq G ( Phi, R) $ This is the subgroup generated by the parent groups, that is, elements of the form $ U_ alpha (R) $ Where $ alpha in Phi $ and $ U_ alpha $ The core group that is assigned $ alpha $,

Whenever $ R = k $ is a field to think about $ E ( Phi, k) $ as an abstract group represented by symbols $ x_ alpha (r) $ With $ alpha in Phi $ and $ r in R $ are subject to the so-called "Steinberg relations". This is the implication 3 on page 21 of this PDF.

For any rings $ R $ the group $ E ( Phi, R) $ I will also satisfy the Steinberg relationship and my question is whether these relationships are sufficient to present them $ E ( Phi, R) $,

One approach to answering this question, of course, is to follow this reference and check whether the hypothesis of $ R $ Being a field was not used for the proof of Corollary 3. It seems to me quite possible to go through the argument, but since I want to use this result, it would be very useful for me if there is already a reference that deals with it explicitly for any ring $ R $so I do not have to retype the argument as an attachment.

Windows Group Rights to Manage Group Policy?

Imagine the following scenario:

The Client Engineering department is responsible for managing all systems that users interactively log in to, including most corporate desktop and laptop computers, RDS servers, and some application servers. You have local administrator rights to all of these systems and full authority to make operational decisions about how they are configured, what software is installed on them, and who can access what.

To do this, the client engineering team must be able to control the group policies for systems in their area of ​​responsibility. The Client Engineering security group has therefore delegated access to the GPO container in the GPMC, as well as the ability to link and unlink GPOs to their managed OUs.

The problem:
Bob (a member of the Client Engineering team) creates a GPO to test some application settings for a project he's working on, and associates it with an OU to test the functionality. Because Bob has created the GPO, he can edit, delete, link, ungroup, and delegate the GPO as needed. However, Bob has neither the rights to manage GPOs created by other teams, nor the privileges to associate his new GPO with containers outside of the delegated OU structure. So far, so good; that is exactly what we want.

Unfortunately, when Bob created the new GPO, Windows added his user account to the ACL of the GPO and not to the Client Engineering group, as specified on the Group Policy Objects GPO tab. Other members of the team can break or unlink other organizational units (because the delegation is from ADUC and not from GPMC). However, Bob is the only person who can edit, delete, or modify permissions on this GPO. No other member of the Client Engineering team can manage this policy unless Bob remembers to explicitly grant privileges to the Client Engineering group, and Bob can not manage policies created by other members of his team unless he does so have done. That's bad – not at all what we want.

How can permissions in AD be set up properly so that members of the Client Engineering security group can create, edit, delete, and delegate GPOs created by them?