* **[HoTT] Topology is Combinatorics over Finite Fields**
**@ 2018-12-20 3:24 José Manuel Rodriguez Caballero**
0 siblings, 0 replies; 1+ messages in thread
From: José Manuel Rodriguez Caballero @ 2018-12-20 3:24 UTC (permalink / raw)
To: HomotopyTypeTheory
[-- 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 --]
^ permalink raw reply [**flat**|nested] 1+ messages in thread

only message in thread, back to index
**Thread overview:** (only message) (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2018-12-20 3:24 [HoTT] Topology is Combinatorics over Finite Fields José Manuel Rodriguez Caballero

Discussion of Homotopy Type Theory and Univalent Foundations
Archives are clonable: git clone --mirror http://inbox.vuxu.org/hott
Newsgroup available over NNTP:
nntp://inbox.vuxu.org/vuxu.archive.hott
AGPL code for this site: git clone https://public-inbox.org/ public-inbox