IUTを読むための用語集資料集スレ

[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
通常表示 512ﾊﾞｲﾄ分割ﾚｽ栞
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｡

52: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2020/06/27(土) 23:02:30.33 ID:jEjJjPRO

>>51
つづき

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. One also distinguishes between fine and coarse moduli spaces for the same moduli problem.

The most basic problem is that of moduli of smooth complete curves of a fixed genus. Over the field of complex numbers these correspond precisely to compact Riemann surfaces of the given genus, for which Bernhard Riemann proved the first results about moduli spaces, in particular their dimensions ("number of parameters on which the complex structure depends").

Genus 1
Main article: Moduli stack of elliptic curves

つづく

http://rio2016.5ch.net/test/read.cgi/math/1592654877/52

149: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2020/07/15(水) 22:22:21.33 ID:hRRJMwM+

>>148 追加

https://en.wikipedia.org/wiki/Tate%27s_algorithm
Tate's algorithm
(抜粋)
In the theory of elliptic curves, Tate's algorithm takes as input an integral model of an elliptic curve E over {\displaystyle \mathbb {Q} }\mathbb {Q} , or more generally an algebraic number field, and a prime or prime ideal p. It returns the exponent fp of p in the conductor of E, the type of reduction at p, the local index
c_p=[E(Q_p):E^0(Q_p)],
where  E^0(Q_p) is the group of Q_p-points whose reduction mod p is a non-singular point.
Also, the algorithm determines whether or not the given integral model is minimal at p, and, if not, returns an integral model with integral coefficients for which the valuation at p of the discriminant is minimal.

Tate's algorithm also gives the structure of the singular fibers given by the Kodaira symbol or Neron symbol, for which, see elliptic surfaces: in turn this determines the exponent fp of the conductor E.

Tate's algorithm can be greatly simplified if the characteristic of the residue class field is not 2 or 3; in this case the type and c and f can be read off from the valuations of j and Δ (defined below).

Tate's algorithm was introduced by John Tate (1975) as an improvement of the description of the Neron model of an elliptic curve by Neron (1964).

Contents
1 Notation
2 The algorithm
3 Implementations

Implementations
The algorithm is implemented for algebraic number fields in the PARI/GP computer algebra system, available through the function elllocalred.

http://rio2016.5ch.net/test/read.cgi/math/1592654877/149

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 0.038s