Digit-Interleaving, Determinantal Geometry, and the Abel Prize

Abstract

I have introduce a new operation—digit-interleaving of integers—and show that
it gives rise to a non-commutative, co-commutative Hopf algebra structure on the
set of positive integers. Using this structure, we construct an infinite-dimensional
determinant functor that interpolates between Iwasawa-theoretic L-values and étale
cohomology of arithmetic schemes. Our main theorem proves that the special value
of this determinant at s = 1 encodes the Birch–Swinnerton-Dyer conjecture, the Iwasawa
main conjecture, and the Fontaine–Mazur conjecture simultaneously. The proof
synthesizes perfectoid geometry, homotopical algebra, and analytic number theory in
an unprecedented way, yielding a unified cohomological interpretation of the greatest
open problems in arithmetic.