[HoTT] Topology is Combinatorics over Finite Fields

[HoTT] Topology is Combinatorics over Finite Fields

[José Manuel Rodriguez Caballero]

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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.

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