Discussion of Homotopy Type Theory and Univalent Foundations
 help / color / mirror / Atom feed
From: "José Manuel Rodriguez Caballero" <josephcmac@gmail.com>
To: HomotopyTypeTheory@googlegroups.com
Subject: [HoTT] Topology is Combinatorics over Finite Fields
Date: Wed, 19 Dec 2018 22:24:30 -0500	[thread overview]
Message-ID: <CAA8xVUiCLDFxL6Op-SdY1+Kbt7YLZPoJKW8xQ8dkg4P2jPhKiA@mail.gmail.com> (raw)

[-- Attachment #1: Type: text/plain, Size: 1387 bytes --]

Hello,
  According to Weil's conjectures (right now, theorems), some topological
invariants have combinatorial interpretations related to finite fields.
Could the slogan "Topology is Combinatorics over Finite Fields" be
justified to some extent?

  I say that a type T is determined by a set S of algebraic equations over
an arbitrary finite field if all the topological invariants of T can be
interpreted in a natural way as the number of solutions of the system S.I
say that a type T is determined by a set S of algebraic equations over an
arbitrary finite field if all the topological invariants of T can be
interpreted in a natural way as the number of solutions of the system S. Is
any type in HoTT determined by a set of algebraic equations over an
arbitrary finite field?

  I know that these questions may be rather ambiguous. I think that Weil's
conjectures are just a particular case of a more general duality between
combinatorics over a finite field and topology, but it is hard to find the
right way to state the problem.

Kind Regards,
José M.

-- 
You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.
To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.

[-- Attachment #2: Type: text/html, Size: 1699 bytes --]

                 reply	other threads:[~2018-12-20  3:24 UTC|newest]

Thread overview: [no followups] expand[flat|nested]  mbox.gz  Atom feed

Reply instructions:

You may reply publicly to this message via plain-text email
using any one of the following methods:

* Save the following mbox file, import it into your mail client,
  and reply-to-all from there: mbox

  Avoid top-posting and favor interleaved quoting:
  https://en.wikipedia.org/wiki/Posting_style#Interleaved_style

* Reply using the --to, --cc, and --in-reply-to
  switches of git-send-email(1):

  git send-email \
    --in-reply-to=CAA8xVUiCLDFxL6Op-SdY1+Kbt7YLZPoJKW8xQ8dkg4P2jPhKiA@mail.gmail.com \
    --to=josephcmac@gmail.com \
    --cc=HomotopyTypeTheory@googlegroups.com \
    /path/to/YOUR_REPLY

  https://kernel.org/pub/software/scm/git/docs/git-send-email.html

* If your mail client supports setting the In-Reply-To header
  via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).