nic – QLogic Fiber Card not working with HYVE-Zeus Server

I have a QLogic QLE2564 Fiber Card that doesn’t seem to be working with my server. I am running windows server 2019 on a Hyve Zeus V1 with a supermicro X9DRD-LF motherboard. When installed, the card is not detected in device manager or when the system boots. All the lights on the card remain on even after boot. I have the card installed in the only pcie slot on the board with a riser. I tested it without the riser and still get the same results. I disabled the onboard gig ports through the bios and rebooted. That did nothing. I don’t have another machine to test the card itself. Is there something in the bios I’m missing or needs a flash? Is the card not compatible or could it be dead?

arithmetic geometry – Hochschild-Serre like spectral sequence for $p$-adic uniformization of special fiber of Shimura variety?

This question follows from my reading of Fargues’ 2004 paper published in Astérisque, whose notations I borrow. One of the central part of the paper is the construction of a Hochschild-Serre type spectral sequence computing the étale (compactly supported) cohomology of the quotient of an analytic space under the action of a discrete group, Théorème 4.5.1. Here, Berkovich’s theory is used. This is then applied to the case of the $p$-adic uniformization of PEL Shimura variety by associated Rapoport-Zink spaces, Théorème 3.2.6 and Théorème 4.5.12. Indeed, if $K = K_pK^p$ denotes a level structure, $phi$ is an isogeny class of abelian varieties with additional structures and $I^{phi}(mathbb Q)$ its automorphism group, then the $p$-adic uniformization is an isomorphism of analytic spaces with various actions
$$I^{phi}(mathbb Q)backslash left(breve{mathcal M}_{K_p}times G(mathbb A_f^p)/K^pright) xrightarrow{sim} mathrm{Sh}_K^{mathrm{an}}(phi)$$
And the left-hand side may be re-written as a union $bigsqcup_{iin I} Gamma_ibackslash breve{mathcal M}_{K^p}$ for some finite number of properly defined discrete subgroups $Gamma_i$ of $I^{phi}(mathbb Q)$ (this requires some choices). Here, $breve{mathcal M}_{K_p}$ is the level-$K_p$ covering of the generic fiber of the Rapoport-Zink space, $mathrm{Sh}_K^{mathrm{an}}(phi)$ is the level-$K_p$ covering of the analytic tube of the stratum $widetilde{S}_{K^p}(phi)$ corresponding to $phi$ inside the special fiber of the Shimura variety ; and the group $G$ is given by the PEL datum. The spectral sequence then takes the following form for $ellnot = p$ :
$$E_2^{p,q} = mathrm{Ext}_{J_b-text{smooth}}^{p}left(mathrm H_c^{2N-q}(breve{mathcal M}_{K_p}widehat{otimes},mathbb C_p,overline{mathbb Q_{ell}})(N), (mathcal A_{rho}^{phi})^{K^p} right) implies mathrm H^{p+q}(mathrm{Sh}_K^{mathrm{an}}(phi),mathcal L_{rho}^{mathrm{an}})$$
where $rho$ is some fixed algebraic representation of $G$ giving rise to a local system $mathcal L_{rho}$ on the Shimura tower, $mathcal A_{rho}^{phi}$ is a space of automorphic representations of $I^{phi}(mathbb Q)$ which are of type $rho$ at infinity and $N$ is the dimension of the Shimura variety. Of course, the spectral sequence comes with compatibility with various actions.

My question is, to what extent does the whole construction rely on
Berkovich’s theory of analytic spaces and étale cohomology ?

Let me be more specific. I denote by $C_0$ the maximal level structure at $p$ (ie. there is no level structure). If I understand correctly, it is necessary to introduce the generic fiber $breve{mathcal M}$ of the Rapoport-Zink space $mathcal{M}$ in order to define the tower $(breve{mathcal M}_{K_p})$ for $K_psubset C_0$ an open compact subgroup. So when one is interested in higher level structures or in the whole tower, analytic spaces seems inevitable. But what if one is only interested in the maximal level $C_0$, it looks like everything can be done at the level of special fibers and fair $overline{mathbb F}_p$-schemes.

Indeed, at maximal level the uniformisation theorem can be staded for the integral models on both sides and not just on the generic fiber. Specializing to the special fiber, we have an isomorphism of $overline{mathbb F}_p$-schemes
$$I^{phi}(mathbb Q)backslash left({mathcal M}_{mathrm{red}}times G(mathbb A_f^p)/K^pright) xrightarrow{sim} widetilde{S}_{K^p}(phi)otimes overline{mathbb F_p}$$
With such an identity, would the spectral sequence constructed by Fargues still work for the special fibers and “classical” étale cohomology, or is there some obstacle that I am not aware of ?

Fiber product formulae for surgery obstructions

Is there a formula for the surgery obstruction of a fiber product of maps assuming the fiber product is also a homotopy equivalence?

In more detail, suppose that $X to Y$ and $Z to Y$ are homotopy equivalences of (topological, say, compact oriented) manifolds. There is a long history of product formulae for surgery obstructions which includes a surgery obstruction for the product map $X times Z to Y times Y$ to be homotopic to a homeomorphism. See for example Section 8 in Ranicki, Algebraic Theory of Surgery II. Applications to Topology.

Suppose I know that the fiber product $X times_Y Z to Y$ is also a homotopy equivalence. (Often it won’t be, but in my case I got lucky.) Is there a formula for the surgery obstruction of this map in terms of those of $X to Y$ and $Z to Y$? I am actually just interested in the case $X times_Y X to Y$, perturbed to make the fiber product transverse and would like to know what are the possibilities for the surgery obstruction of this map. (Could it be anything?)

rt.representation theory – Are there cases in which the Weyl group _does_ act on the flag variety/springer fiber?

In nearly every reference on the classical springer correspondence (for example Chriss/Ginzburg’s book on Complex Geometry) it is stated that the action of the Weyl Group on the homology of the springer fiber is not induced by an action of the Weyl group on the fiber itself. But I couldn’t find any reference or general statement that would make this precise (and I’m just learning about geometric representation theory so I don’t have any good intuition/working knowledge).

For concreteness (and I think this should be a simpler case), consider the springer fiber over zero — then $mathcal{B}_0 = mathcal{B} = G/B$ is the flag varitey (where $B$ is a Borel subalgebra). Now there is an action of the Weyl group $W$ on the quotient $G/T$ (where $Tsubseteq B$ is a maximal torus, which allows to write $W = N_G(T)/T$). Now in Yun’s notes, (1.5.4), he writes that the map $G/Tto G/B$ is an “affine space bundle”, that this implies that the their homologies are isomorphic and that under this isomorphism, the action of $W$ on $H(G/T)$ gives the springer action of $W$ on $H(mathcal{B})$ (I couldn’t find a reference for that though). But I don’t see why there should be no way to use this projection to define an action of $W$ on $mathcal{B}$.
Also, in “Schubert cells and cohomology of the spaces $G/P$” (1973), Bernstein Gelfand and Gelfand construct in chapter 5 a correspondence that gives rise to the springer action. I was hoping that this very explicit construction in the paper would shed some more light on what’s going on, but I haven’t been able to do that myself.

Any help, and also references, are really appreciated.

Some questions about SFP+ fiber networking in general

Ok. So I’m completely new to the world of fiber. I’ve used Ethernet all my life.
We’re looking to upgrade some of our infrastructure, and I’m thinking of getting a few of these:

10G Dual SFP+ NIC

for our servers and a couple of these to connect them

POE Switch with 4x10G SFP+ Uplinks

But I’m a bit confused about this transceiver stuff.
Do these NICs and Switches just have holes in them that I’m supposed to put transceivers in?
I’m used to regular switches with regular ethernet, I get a patch cable rated for the speed I want and plug it in at each point and call it a day.

I know I want 10G Fiber to and from my servers, and then 1G Ethernet is fine everywhere else.
What am I missing? Am I just worrying for nothing?
What kinds of wires do I even need? There are so many, and with ethernet I just know all this stuff already. But I don’t even know what to search for when it comes to fiber.

internet – Comcast upgraded my neighborhood cables to fiber optics and now I’m getting 5.5 GBPS upload speeds over WIFI. What is going on?

Link to speed test screenshot

A few weeks ago Comcast upgraded my neighborhood cable infrastructure from coax copper to fiber optics. Since then my network connectivity has not been great… Initially throughput was about 10% of max speeds both down and up. Tech support did some modifications on their end and download speeds are in line with expectations about 70% of the time. I was also experiencing exceptionally weird upload speeds. My upload speeds have typically been initially spiking to about 2-3 gigabits per second, crash, and then reset to 40 megabits per second. I’ve been able to replicate this on multiple devices too. It’s also been a challenge doing work remote because my servers/services have no clue what’s going on with my wonky connection and drop my file uploads like it’s hot.

Now here is where things get really weird. After ascending the many tiers of tech support to try and resolve my problems, they did some more work to my building’s (multi-unit dwelling consisting of about 20 condos) physical network yesterday afternoon and it seems my problems are more pronounced. Last night I got 5.5 GBPS upload speeds over WIFI.

But does anyone have any clue as to what might be problem??? All I want is my network connection to be steady and consistent. I’m not pointing fingers, something very weird is going on here. I’m just hoping someone has some idea of what to do next. I’m at a loss as to what’s going on. Comcast also hasn’t gotten back to me either since my most recent update was outside of working hours last night.

Here are some extra details:

  • Primary computer: Surface Book 3 (802.11ax capable, everything up to date)
  • Modem/Router: Netgear CAX80 (802.11ax capable, DOCSIS 3.1, running the latest firmware, remotely rebooted at least 20 times and counting)
  • Internet plan: Comcast 1.2 GBPS downloads, 40 MBPS uploads

ipv6 – How do I port forward a Minecraft server on Google Fiber?

I need to port forward the following ports:

IPv4: 19132
IPv6: 19133
IPv4: 34578
IPv6: 57597

all on TCP & UDP.

I need to do this because I want to port forward a Dedicated Minecraft Bedrock Server, following instructions here.

I did a quick Google search and found this Google article, but I’m kind of confused – there are so many options!

I did this in the Fiber setup, but it didn’t seem to work…

I port forwarded on the device of my internet’s name, with Universal Plug and Play set to on, choosing the IP address of my Ubuntu server (the IP with letters and colon; the one that is very long), forwarding a single port 19132->19133 (I’m not doing the second port yet), with protocol TCP & UDP.

I think I’m getting the ports wrong (IPv4 or IPv6?), or maybe the “Single port” selection, but I have no idea!

What am I doing wrong?

Appreciate the help!

at.algebraic topology – Homology of a fiber as a cotorsion product

Let $K$ be a field. For any differentially graded coalgebra $A$ over $K$, any differentially graded right $A$-comodule $M$ over $K$ and any differentially graded left $A$-comodule $N$ over $K$ let
$mathrm{Cotor}_A(M,N)$ denote the cotorsion product of $M$ and $N$ relative to $A$.

The graded $K$-vector space $mathrm{Cotor}_A(M,N)$ is by definition the homology of the totalization of the cosimplicial cochain complex over $K$ with $n$-th term $M otimes A^{otimes n} otimes N$,
where the tensor product is in cochain complexes over $K.$

Let $X to Y$ be a Serre fibration between connected spaces and $F$ its fiber over a given point $y$ of $Y.$

If $Y$ is simply connected, by a theorem of Eilenberg and Moore there is a canonical isomorphism
H_*(F;K)cong mathrm{Cotor}_{C_*(Y; K)}(C_*(X; K),C_*(*; K)), (**)

where $C_*(-;K)$ are singular chains with coefficients in the field $K.$

Can we replace the condition that $Y$ is simply connected by a weaker condition?

For example, is there still a canonical isomorphism $(**)$ if $Y = BG = K(G,1) $ for $G$ a derived p-complete abelian group?

at.algebraic topology – Isotopies, Fiber Bundles and Selection Theorems

The following problem is a culmination of a few questions I’ve asked the last two months, and it’s still giving me some issues. I think I know the right way to solve it, but I’m having trouble with the details; my idea can be formulated in terms of selection theorems or fiber bundles.

Let $X subset mathbb{R}^n$ be any subspace, and let $I = (0,1)$. By a proper isotopy of $X$ I mean a continuous function $F: X times I rightarrow mathbb{R}^n$ such that for each $t in I$, $f_t := F|_{X times lbrace t rbrace}$ is an embedding and $f_0 = text{id}_X$. By an ambient isotopy I mean an isotopy on all of $mathbb{R}^n$.

If $F$ is a proper isotopy of a tamely embedded copy $X$ of $mathbb{S}^{n-1}$ in $mathbb{R}^n$, does $F$ extend to an ambient isotopy?

As noted in the answer here, this will be true as long as $F$ can be extended in some neighborhood of $X$.

I’m mostly interested in the case for the plane. In fact, for the plane it’s already known to be true, but the proof is very difficult. There was a follow-up paper where they defined a notion of length for plane curves that extended to unrectifiable curves, and which behaved continuously with respect to uniform convergence of compact sets (so basically, they didn’t require 0-regular convergence); between the preprint, the Annals paper and the follow-up they gave three different arguments, but all hinged on analytically controlling crosscuts using geometric function theory. My idea is also to use cross-cuts, but not to construct an explicit isotopy.

Using results from the Kirby-Edwards paper linked in the previous MO thread, and a ‘canonical’ Alexander-Pontryagin Duality Theorem in the plane, you can prove the isotopy extension theorem for compact, connected subsets of $mathbb{R}^2$ in a different way from the case for the circle (though it’s also fairly complicated, and is ill-suited to the generalizations they obtained in the follow-up).

What I’d like to do is get the case for the circle using some selection theorem, esp. the Michael Selection Theorem (or even better, a selection theorem whose proof is actually reasonable). To do this, let $D$ be a large, closed ball around the trace of $X$ under $F$. By the Annulus Theorem, each region between $partial(D)$ and $f_t(X) := X_t$ is a closed annulus, call it $A_t$.

For any $A_t$ there are many ways to partition it into crosscuts, so that each crosscut has one endpoint on each boundary component. By a crosscut, I mean an embedded copy of $I$. Let $mathcal{C}_t$ denote the collection of such partitions on $A_t$, and let $mathcal{C} = cup mathcal{C}_t$. Then what we want is a continuous selection of cross-cut decompositions, one for each $A_t$. To be precise, we should probably consider a family of parameterized cross-cut decompositions, so that each has a time parameterization (that will be our way of getting around $0$-regular convergence issues).

This is equivalently a fiber bundle problem on $mathbb{A}^n times I$ in the following sense. We have two cylinders, one the usual smooth cylinder, and the other one just some Jordan mess, as the boundaries. Can we warp it into the standard, smooth representative in a way that’s slice?

Long story short, the problem for the selection method is:

How do you topologize $mathcal{C}$ to apply the Michael Selection Theorem?

The problem for the fiber bundle method is:

If $mathbb{A}^n times I subset mathbb{R}^{n+1}$ is a bundle over $I$ whose slices $mathbb{A}^n_t$ are contained in hyperplaces orthogonal to the $(n+1)$-axis, is there an isotopy to the standard smooth (thickened) cylinder that’s slice? In other words, $f_s(mathbb{A}^n_t) subset mathbb{A}^n_t$ for all $s$ and $t$.

Thanks, appreciate any help at all!

ag.algebraic geometry – Mori fiber space in dimension $2$ over a point is $mathbf P^2$

Let $k$ be an algebraically closed field. Let $X$ be a surface over $k$. Let $pi: X to S$ be an extremal contraction. It is well-known that if $dim(S) = 0$, then $X cong mathbf P^2$. I wonder if we can prove this using Mori’s result: A variety $X$ is isomorphic to the projective space if and only if $-K_X$ is ample and every non-constant morphism $mathbf P^1 to X$ is very free.