I recall having read, some time ago, a beautiful and poetic opening of an article (or was it a book?). From memory, it was by Shigefumi Mori, and talked about the (mathematical) universe consisting of two hemispheres, a real and a p-adic; somehow meeting at the equator. We mere humans should strive to contemplate both sides and their connections.


I have tried to locate the precise reference of this text, including some of Mori's papers, but failed. In fact, I'm not anymore sure it was Mori.


Does some kind soul know which reference I'm trying to recall?



Mori: p-adic and real hemispheres of the mathematical universe?

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> 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'. 
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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.) 


