[過去ﾛｸﾞ] IUTを読むための用語集資料集スレ (1002ﾚｽ)
上下前次1-新
抽出解除 必死ﾁｪｯｶｰ(本家) (べ) 自ID ﾚｽ栞 あぼーん
このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索 歴削→次ｽﾚ 栞削→次ｽﾚ 過去ﾛｸﾞﾒﾆｭｰ
ﾘﾛｰﾄﾞ規制です｡10分ほどで解除するので､他のﾌﾞﾗｳｻﾞへ避難してください｡
179(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)09:47 ID:2Y0qBKwb(1/9) AAS
>>173 補足
新しい動きはもう始まっている
例えば下記
"In this paper I consider a different approach to this problem of understanding the fluidity of ring structures and in particular to the problem of quantifying the fluidity of the additive structures on the set OΔK ∪ {0} for a p-adic field K.
I began thinking of this problem in Kyoto (Spring 2018) and my preoccupation with it became more or less permanent on my return from Kyoto."
とかあるよね。Kirti Joshi氏は、自分なりに理解しようとしているんだ！
"Mochizuki’s anabelian reconstruction yoga (see [22] and its references) provides"とかある
省15
180(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)09:47 ID:2Y0qBKwb(2/9) AAS
>>179
つづき
; later he has refined this result and shown that K may be recovered from the topological group GK and one Lubin-Tate character of GK (see [14] and [20]).
On the other hand, given a padic field K1, the Jarden-Ritter Theorem (see [8]) provides a characterization of all p-adic fields
K2 such that one has a topological isomorphism GK2 ' GK1 of their absolute Galois groups and
it is well-known that for every prime p, pairs of fields with this property always exists.
Mochizuki’s anabelian reconstruction yoga (see [22] and its references) provides, starting with
省12
181(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)09:48 ID:2Y0qBKwb(3/9) AAS
>>180
つづき
In this paper I consider a different approach to this problem of understanding the fluidity of ring structures and in particular to the problem of quantifying the fluidity of the additive structures on the set OΔK ∪ {0} for a p-adic field K.
I began thinking of this problem in Kyoto (Spring 2018) and my preoccupation with it became more or less permanent on my return from Kyoto.
The idea, which I elaborate here, occurred to me in a recent lecture by Michael Hopkins at the Arizona Winter School (2019).
In one of his lectures, Hopkins narrated an anecdote about Daniel Quillen’s discovery of the role of formal groups in topological cohomology theories:
in particular Quillen’s assertion (to Hopkins) that “as addition rule for Chern classes fails to hold,
省3
182: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)09:49 ID:2Y0qBKwb(4/9) AAS
>>181
つづき
As was also pointed out to me by Taylor Dupuy, Mochizuki recognized a long time ago (see for
instance [15, Section 4]) that arithmetic applications of anabelian geometry lead naturally to the
deep and difficult problem of understanding the line bundles and (Arakelov) degrees (or Arakelov
Chern classes) in the presence of anabelian variation of ring structures and he resolved this problem
by means of his theory of Frobenioids and realified Frobenioids [18] and Arakelov-Hodge theoretic
省5
183: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)15:00 ID:2Y0qBKwb(5/9) AAS
>>179
>新しい動きはもう始まっている
>例えば下記
>"In this paper I consider a different approach to this problem of understanding the fluidity of ring structures and in particular to the problem of quantifying the fluidity of the additive structures on the set OΔK ∪ {0} for a p-adic field K.
I> began thinking of this problem in Kyoto (Spring 2018) and my preoccupation with it became more or less permanent on my return from Kyoto."
>とかあるよね。Kirti Joshi氏は、自分なりに理解しようとしているんだ！
これがあるべき姿だと思う
省8
185(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)17:46 ID:2Y0qBKwb(6/9) AAS
>>166 追加
”Shimura curves”
外部ﾘﾝｸ:www.math.columbia.edu
Chao Li's homepage
外部ﾘﾝｸ[html]:www.math.columbia.edu
Shimura curves
In the 60s, Shimura studied certain algebraic curves as analogues of classical modular curves in order to construct class fields of totally real number fields. These curves were later coined "Shimura curves" and vastly generalized by Deligne. We will take a tour of the rich geometry and arithmetic of Shimura curves. Along the way, we may encounter tessellations of disks, quaternion algebras, abelian surfaces, elliptic curves with CM, Hurwitz curves ... and the answer to life, the universe and everything.
省14
186(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)17:47 ID:2Y0qBKwb(7/9) AAS
>>185
つづき
外部ﾘﾝｸ:ja.wikipedia.org
志村多様体（Shimura variety）とは代数多様体であってモジュラー曲線の高次元化とみなせるような整数論で重要な対象である。
歴史
「志村多様体」と言う命名はピエール・ドリーニュ(Pierre Deligne)が導入し、彼は志村理論の中で独立した抽象的な形をしている部分の研究を推し進めた。ドリーニュの定式化では、志村多様体はホッジ構造のあるタイプのパラメータ空間である。このようにして、彼らは、レベル構造を持つ楕円曲線のモジュライ空間がそうであったように、モジュラ曲線の自然に高次元への一般化を作り出した。
例
省3
187: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)17:48 ID:2Y0qBKwb(8/9) AAS
>>186
つづき
外部ﾘﾝｸ:en.wikipedia.org
Shimura variety
In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties are not algebraic varieties but are families of algebraic varieties. Shimura curves are the one-dimensional Shimura varieties.
History
In Deligne's formulation, Shimura varieties are parameter spaces of certain types of Hodge structures. Thus they form a natural higher-dimensional generalization of modular curves viewed as moduli spaces of elliptic curves with level structure.
省4
188: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/19(日)17:53 ID:2Y0qBKwb(9/9) AAS
>>185
”Shimura curves”は、志村多様体の１次元版か
でも、複素１次元ぽいな
”ピエール・ドリーニュ(Pierre Deligne)が導入し、・・彼らは、レベル構造を持つ楕円曲線のモジュライ空間がそうであったように、モジュラ曲線の自然に高次元への一般化を作り出した。”
とあるから、楕円曲線を拡張したものかね？（＾＾
” Zeta functions of Shimura varieties associated with the group GL2 over other number fields and its inner forms (i.e. multiplicative groups of quaternion algebras) were studied by Eichler, Shimura, Kuga, Sato, and Ihara.”
Sato＝佐藤幹夫かな？
上下前次1-新書関写板覧索設栞歴
ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ
ぬこの手 ぬこTOP 0.050s