JMSJ 論文賞受賞者のことば
JMSJ とは，日本数学会の出版する学術雑誌 Journal of the Mathematical Societyof Japan の略称です．JMSJ 論文賞は，授賞年前年の JMSJ に掲載された論文のうち特に優れたもの（3 篇以内）の著者に贈られる賞です．
2013 年 JMSJ 論文賞は以下の 2 篇に贈られました．
著者：柳田 伸顕 氏（Nobuaki Yagita，茨城大教育）
論文題目：Chow rings of nonabelian p-groups of order p3 , JMSJ, 64 (2012), 507–531.
受賞者のことば：悪い論文の見本のような自分の論文が受賞し，恐縮しています．論文作り始めのころは，それなりの事が出来たと思いましたが，よく見ると簡単な話しになっていき，こんな安易な話では Journal は無理だろうなと思ったことを思い出します．しかも，小さな非可換 p-群のコホモロジー環と言う特殊な話題なので受賞には驚いています．
しかし今後もこの事を励みにして勉強を続けていけたら幸せと思います．最後に一緒に群のコホモロジーを勉強し，色々教えてもらった手塚康誠氏と何でも話せた同僚で去年なくなった岡安隆氏に感謝の気持ちを述べたいと思います．
著者：Gopal Prasad 氏（Univ. of Michigan），Sai-Kee Yeung 氏（Purdue Univ.）
論文題目：Nonexistence of arithmetic fake compact Hermitian symmetric spaces oftype other than An (n ≤ 4), JMSJ, 64 (2012), 683–731.
受賞者のことば：
Impression/Acknowledgement
It is a great honor for the authors that our paper was awarded 2013 JMSJ Outstanding Paper Prize. This paper is the third installment of a project initiated bythe authors. It began with a paper of the authors on classiﬁcation of fake projective planes. A fake projective plane is a smooth complex projective algebraic
surface with the same Betti numbers as the complex projective plane but which is
not biholomorphic to it. The ﬁrst example of such a surface was constructed byD. Mumford in 1979 using p-adic uniformization. In the ensuing years, two more
examples were constructed by M. Ishida and F. Kato using Mumford’s method, andone more by J. Keum. Fake projective planes are interesting because they have thesmallest possible Euler number among all smooth surfaces of general type. It isknown that a fake projective plane is the quotient of the complex two ball by anarithmetic subgroup of the automorphism group of the latter.

In a paper which appeared in Inventiones Mathematicae vol. 168 (Addendum inibid. vol. 182), the authors devised a scheme to classify and construct all fake projective planes. These surfaces were classiﬁed into twenty eight classes, with explicit
examples given in each class. The authors also showed that a complete list of fakeprojective planes will be obtained once all subgroups of some predetermined smallindex of certain arithmetic subgroups of P U (2, 1) are enumerated. This enumeration was done by D. Cartwright and T. Steger using long and very clever computerassisted computations. In this way, they found that altogether there are precisely
100 fake projective planes.
A natural question is whether similar manifolds exist in higher dimensions. This
led to the second paper of the authors which appeared in American Journal of Mathematics vol. 131. In this paper, the authors considered arithmetic fake projective
spaces and fake grassmanians. The authors classiﬁed such manifolds and constructedthe ﬁrst examples of fake projective four spaces and fake Grassmanians.
From the above two papers, it became clear that it would be interesting to classify
all “arithmetic fake compact Hermitian symmetric spaces”. This led us to the paper
which has appeared in JMSJ last year. In this paper, we have considered which
compact hermitian symmetric spaces admit an arithmetic fake analogue. We have
proved in this paper that arithmetic fake compact hermitian symmetric spaces canarise only from the groups SU (p, q) with p + q ≤ 5. The paper provides an approach
to list locally Hermitian symmetric spaces of suﬃciently small volume.
Throughout the project, the authors were greatly encouraged by the interests ofcolleagues from Japan. Professor S. Kondo organized a conference on fake projective
planes at Nagoya University in 2006, just after our ﬁrst paper was completed. We
were invited to give talks at Nagoya, Kyoto, Osaka, Tokyo and several other places
in Japan and we were touched by the warm hospitality of our hosts.