[過去ﾛｸﾞ] 現代数学の系譜 工学物理雑談 古典ガロア理論も読む79 (1002ﾚｽ)
上下前次1-新
抽出解除 ﾚｽ栞

---

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｡

---

405(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/12/14(土)10:28 ID:s6Tab8iq(3/13) AAS
>>404
つづき

Introduction
Many writers have mused about algebraic geometry over deeper bases than the
ring Z of integers. Although there are several, possibly unrelated reasons for this,
here I will mention just two. The first is that the combinatorial nature of enumeration formulas in linear algebra over finite fields Fq as q tends to 1 suggests that,
just as one can work over all finite fields simultaneously by using algebraic geometry over Z, perhaps one could bring in the combinatorics of finite sets by working
over an even deeper base, one which somehow allows q = 1. It is common, following Tits [60], to call this mythical base F1, the field with one element. (See also
Steinberg [58], p. 279.) The second purpose is to prove the Riemann hypothesis.
With the analogy between integers and polynomials in mind, we might hope that
省7

---

406: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/12/14(土)10:29 ID:s6Tab8iq(4/13) AAS
>>405
つづき

The most obvious way of doing this is to consider weaker algebraic structures
than rings (commutative, as always), such as commutative monoids, and to try using them as the affine building blocks for a more rigid theory of algebraic geometry.
This has been pursued in a number of papers, which I will cite below. Another natural approach is motived by the following question, first articulated by Soul´e [57]:
Which rings over Z can be defined over F1? Less set-theoretically, on a ring over
Z, what should descent data to F1 be?
The main goal of this paper is to show that a reasonable answer to this question
is a Λ-ring structure, in the sense of Grothendieck’s Riemann?Roch theory [31].
More precisely, we show that a Λ-ring structure on a ring can be thought of as
省9

---

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 0.042s