https://matpitka.blogspot.com/2017/10/could-precursors-of-perfectoids-emerge.html

Thursday, October 12, 2017

Could the precursors of perfectoids emerge in TGD?

The work of Peter Stolze based on the notion of perfectoid has raised a lot of interest in the community of algebraic geometers. One application of the notion relates to the attempt to generalize algebraic geometry by replacing polynomials with analytic functions satisfying suitable restrictions. Also in TGD this kind of generalization might be needed at the level of M4× CP2 whereas at the level of M8 algebraic geometry might be enough. The notion of perfectoid as an extension of p-adic numbers Qp allowing all p:th roots of p-adic prime p is central and provides a powerful technical tool when combined with its dual, which is function field with characteristic p.

Could perfectoids have a role in TGD? The infinite-dimensionality of perfectoid is in conflict with the vision about finiteness of cognition. For other p-adic number fields Qq, q≠ p the extension containing p:th roots of p would be however finite-dimensional even in the case of perfectoid. Furthermore, one has an entire hierarchy of almost-perfectoids allowing powers of pm:th roots of p-adic numbers. The larger the value of m, the larger the number of points in the extension of rationals used, and the larger the number of points in cognitive representations consisting of points with coordinates in the extension of rationals. The emergence of almost-perfectoids could be seen in the adelic physics framework as an outcome of evolution forcing the emergence of increasingly complex extensions of rationals.

See the article Could the precursors of perfectoids emerge in TGD?.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

32 comments:

Anonymous said...

El cambio muscular pᥙede cuerpo de 1 a 1,5% dе incremento en estado mensual.
Ꭼn ⅼos gimnasios regularmente һay una afición bastardo
ɑ actuar máѕ ejercicios ԁe lɑ рarte líԁer ү
se һace excepto pomposidad еn los grupo
inferiores.

Anonymous said...

El cambio muscular puede cuerpo de 1 а 1,5% de incremento en estɑdo mensual.
En ⅼoѕ gimnasios regularmente һay una afición bastardo a actuar más ejercicios ԁе
la parte líder ʏ se hаce excepto pomposidad en loѕ grupo inferiores.

Anonymous said...

Aun justamente, el Karma ocupa a salvo área que cualquier ideal DJI Phantom y que el
Yuneec Typhoon H, que requieren implicar cajas casi del par del pandeo.
El DJI Phantom 4 Pro es un dron más acondicionado para cineastas y fotógrafos avanzados.

Anonymous said...

Aun justamente, el Karma ocupa a salvo área que cualquier ideal DJI Phantom y
que el Yuneec Typhoon H, que requieren implicar cajas casi del par del pandeo.

El DJI Phantom 4 Pro es un dron más acondicionado para cineastas
y fotógrafos avanzados.

Anonymous said...

Awesome blog! Is your theme custom made or did you download it from somewhere?
A theme like yours with a few simple tweeks would really make my blog
stand out. Please let me know where you got your design. Many thanks

Anonymous said...

Awesome blog! Is your theme custom made or did you download it
from somewhere? A theme like yours with a few simple tweeks would
really make my blog stand out. Please let me know where
you got your design. Many thanks

Anonymous said...

Currently it looks like Wordpress is the top blogging
platform available right now. (from what I've read) Is that what you're using on your blog?

Matti Pitkänen said...

No. I have not used it.

Anonymous said...

Glad to be one of several visitants on this awesome website
:D.

Anonymous said...

Glad to be one of several visitants on this awesome website :D.

Anonymous said...

Rattling instructive and excellent complex body part of articles, now
that's user pleasant (:.

Anonymous said...

Rattling instructive and excellent complex body part
of articles, now that's user pleasant (:.

Anonymous said...

Thank you for sharing your thoughts. I really appreciate
your efforts and I am waiting for your further post thank
you once again.

Anonymous said...

Thank you for sharing your thoughts. I really appreciate your efforts and I am
waiting for your further post thank you once again.

Anonymous said...

Thank you for sharing your thoughts. I really appreciate your
efforts and I am waiting for your further post thank you once again.

Anonymous said...

It has miraculous capabilities to detoxify the blood.

Dry berries are still slightly bitter, but they develop a sticky-candy
taste and consistency. Researchers praise goji berries for his or
her unimaginable antifungal capabilities.

Anonymous said...

It has miraculous capabilities to detoxify the blood.

Dry berries are still slightly bitter, but they develop
a sticky-candy taste and consistency. Researchers praise goji berries for
his or her unimaginable antifungal capabilities.

Anonymous said...

Excellent post. I was checking constantly this weblog
and I am inspired! Very useful information specifically the last phase :) I deal with such info much.
I was seeking this certain info for a long time. Thanks and
best of luck.

Anonymous said...

Excellent post. I was checking constantly this weblog and I am
inspired! Very useful information specifically the last phase :) I deal with such info much.
I was seeking this certain info for a long time. Thanks and best
of luck.

Anonymous said...

I'm not sure where you are getting your info, but great topic.

I needs to spend some time learning more or understanding more.
Thanks for excellent information I was looking for this info for my mission.

Anonymous said...

I'm not sure where you are getting your info, but great
topic. I needs to spend some time learning more or understanding
more. Thanks for excellent information I was looking for this info for my mission.

Anonymous said...

Hmm is anyone else experiencing problems with the pictures on this blog loading?
I'm trying to figure out if its a problem on my end
or if it's the blog. Any feedback would be greatly appreciated.
best cbd oil buy cbd oil cdb oils cbd tinctures

Anonymous said...

Hmm is anyone else experiencing problems with the pictures on this blog loading?
I'm trying to figure out if its a problem on my end or if it's the
blog. Any feedback would be greatly appreciated. best cbd oil buy cbd oil cdb
oils cbd tinctures

Anonymous said...

If you want to increase your experience only keep visiting this site and be updated with
the most recent news update posted here. cbd oil at walmart cannabis oil cbd
vape

Anonymous said...

If you want to increase your experience only keep visiting this site
and be updated with the most recent news update
posted here. cbd oil at walmart cannabis oil cbd vape

Anonymous said...

Hi there, its fastidious piece off writing regarding media print, we all be aware of
media is a great source of facts.

Anonymous said...

I am regular visitor, how are you everybody? This piece of writing posted at this site is actually pleasant.

Anonymous said...

Hello, yup this post is really good and I have learned
lot of things from it concerning blogging. thanks. see here Find Out
More Discover More Here More Help pop over here imp source have a peek at these guys best site additional resources wikipedia reference hop over to this site visit this site right
here my review here click here for more info have
a peek at these guys

Anonymous said...

Hello, yup this post is really good and I have learned lot of things from it concerning blogging.
thanks. see here Find Out More Discover More Here More Help pop over here imp source
have a peek at these guys best site additional resources wikipedia
reference hop over to this site visit this site right here my
review here click here for more info have a peek at these guys

Anonymous said...

look what i found check my reference browse around these guys take a
look at the site here visit the website click here to read investigate this site check this link right here now i loved this look at this website Related Site More Help click
here to find out more Learn More Here special info

Anonymous said...

Online bettors can also use income transfer solutions, wire transfers and funds orders.

Anonymous said...

I'm really enjoying the theme/design of your site.

Do you ever run into any web browser compatibility issues?
A handful of my blog readers have complained about my
blog not working correctly in Explorer but looks great in Safari.
Do you have any suggestions to help fix this issue?