As the night sky, mathematics has two hemispheres; the archimedean hemisphere and the non-archimedean hemisphere. For some reasons, the latter hemisphere is usually under the horizon of our world, and the study of it is historically behind the study of the former. [...] The aim of this paper is [...] to discuss that we can see an arm of a big galaxy, the galaxy of $p$-adic zeta elements, in the non-archimedean hemisphere of zeta values, but that the total shape of this galaxy is still under the horizon. Precisely speaking, we expect the following: As all automorphic representations have zeta functions with values in $\mathbb{C}$, all Galois representations of number fields with coefficients in any $p$-adic ring $\Lambda$ have $p$-adic zeta elements which are canonical bases of some invertible $\Lambda$-modules. [...] The harmony between the two worlds should be called the generalized Iwasawa theory or generalized Deligne-Beilinson conjectures on zeta values. For [the] Riemann zeta function and Dirichlet $L$-functions, Iwasawa theory is the best theory at present for the arithmetic of zeta values. How nice it would be if we can construct the Iwasawa theory of Hasse-Weil $L$-functions. // Where is the homeland of zeta values to which the true reason of celestial phenomena of zeta values are attributed? How can we find a galaxy train [Mi*] to approach it, which runs through the galaxy of $p$-adic zeta elements and whose engine is the theory of $p$-adic periods? I imagine that one coach of the train has the name 'the explicit reciprocity law of $p$-adic Galois representations'.
This is Kazuya Kato speaking of $\zeta$. The reference is the following: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via $B_{
\mathrm{dR}}$, Part I, in: Arithmetic Algebraic Geometry, LNM 1553 (1993). More of this zeta poetry, in a more elementary mathematical level, can be found in the three small volumes Number Theory 1-3 (ed. Kato, Kurihara and Saito), published in the Translations of Mathematical Monographs series.
Mori, incidentally, is linked to a term called a Mori dream space in the minimal model program. He did make a wonderful use of positive characteristic (if not $p$-adic methods) in his work in complex geometry, and I thought this and the association to dream spaces could be partly responsible for why you thought of him here.
With [Mi*] in the above, Kato quotes a Japanese poet, Miyazawa K. (A night on the galaxy train, written circa 1924.)
