Auswahl Schwarzes Brett Aktion im Forum Suche Kontakt Für Mitglieder Mathematisch für Anfänger Wer ist Online | |
| Autor |
 Invariantes Differential einer Formalen Gruppe |
|
xiao_shi_tou_
Senior 
Dabei seit: 12.08.2014
Mitteilungen: 752
Aus: Bonn
 | \(\begingroup\)\(\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\mod}{mod}
\DeclareMathOperator{\codim}{codim}
\DeclareMathOperator{\log}{log}
\DeclareMathOperator{\coker}{coker}
\DeclareMathOperator{\Ob}{Ob}
\DeclareMathOperator{\Emb}{Emb}
\DeclareMathOperator{\Tr}{Tr}
\DeclareMathOperator{\scale}{scale}
\DeclareMathOperator{\Sper}{Sper}
\DeclareMathOperator{\vol}{vol}
\DeclareMathOperator{\Cl}{Cl}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\ord}{ord}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\rad}{rad}
\DeclareMathOperator{\char}{char}
\DeclareMathOperator{\Proj}{Proj}
\DeclareMathOperator{\length}{length}
\DeclareMathOperator{\locArt}{locArt}
\DeclareMathOperator{\Ass}{Ass}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\Pic}{Pic}
\DeclareMathOperator{\Spec}{Spec}
\DeclareMathOperator{\Gal}{Gal}
\DeclareMathOperator{\Hom}{Hom}
\newcommand{\tfae}{\textbf{T.F.A.E.}}
\newcommand{\ndownlong}[2]{#1\ -\!\!\!\rightharpoonup\!\leftharpoondown\!\to\! #2}
\newcommand{\shso}{\udl{\text{Sheaves on}}}
\newcommand{\shs}{\udl{\text{Sheaves}}}
\newcommand{\GG}{\c{G}}
\newcommand{\ush}[1]{\udl{\text{Sheaf}}(#1)}
\newcommand{\sh}{\udl{\text{Sheaf}}}
\newcommand{\rr}{/\!\!/}
\newcommand{\proof}{\udl{\mathscr{P}\mathscr{r}\mathscr{o}\mathscr{o}\mathscr{f}:}}
\newcommand{\defeq}{\overset{\mathscr{D}\mathscr{e}\mathscr{f}.}{=\!=}}
\newcommand{\set}[2]{\{#1\mid #2\}}
\newcommand{\SS}{\mathscr{S}}
\newcommand{\noem}{\not=\emptyset}
\newcommand{\DD}{\c{D}}
\newcommand{\BB}{\c{B}}
\newcommand{\Pr}{\ff{P}}
\newcommand{\exact}[3]{0\to #1\to #2\to#3\to 0}
\newcommand{\qed}{\ff{Q}.\ff{E}.\ff{D}.}
\newcommand{\wt}[1]{\widetilde{#1}}
\newcommand{\spr}[1]{\Sper(#1)}
\newcommand{\nuplong}[2]{#1\ -\!\!\!\rightharpoondown\!\leftharpoonup\!\to\! #2}
\newcommand{\ndownloong}[2]{#1 -\!\!\!-\!\!\!\rightharpoonup\!\leftharpoondown\!\!\!\longrightarrow \!#2}
\newcommand{\bop}{\bigoplus}
\newcommand{\eps}{\epsilon}
\newcommand{\K}{\mathbb{K}}
\newcommand{\ip}{\langle -,- \rangle}
\newcommand{\ipr}[2]{\langle #1,#2 \rangle}
\newcommand{\vth}{\vartheta}
\newcommand{\pprod}{\prod_{v\in\ff{M}_\K}}
\newcommand{\pfam}[1]{(#1)_{v\in\ff{M}_\K}}
\newcommand{\finfam}[1]{(#1)_{i=1}^n}
\newcommand{\fam}[1]{(#1)_{i\in I}}
\newcommand{\jfam}[1]{(#1)_{j\in J}}
\newcommand{\kfam}[1]{(#1)_{k\in K}}
\newcommand{\nfam}[1]{(#1)_{n\in \N}}
\newcommand{\udl}[1]{\underline{#1}}
\newcommand{\Uij}{U_i\cap U_j}
\newcommand{\vpi}{\varphi_i}
\newcommand{\vpj}{\varphi_j}
\newcommand{\psij}{\psi_{i,j}}
\newcommand{\CC}{\c{C}}
\newcommand{\nsum}{\sum_{n\in\N}}
\newcommand{\twist}[1]{\c{O}_{\mathbb{P}_k^n}(#1)}
\newcommand{\prj}[1]{\Proj (#1)}
\newcommand{\part}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\kxn}{k[x_0,\pts,x_n]}
\newcommand{\ka}{\kappa}
\newcommand{\pr}{\mathfrak{p}}
\newcommand{\abs}[1]{\left| #1\right|}
\newcommand{\ab}{\left|-\right|}
\newcommand{\eps}{\epsilon}
\newcommand{\N}{\mathbb{N}}
\newcommand{\KX}{K[X]}
\newcommand{\cov}{\c{U}}
\newcommand{\ff}[1]{\mathfrak{#1}}
\newcommand{\legendre}[2]{\left(\frac{#1}{#2}\right)}
\newcommand{\ANF}{K/\Q}
\newcommand{\GFF}{F/{\F_p(t)}}
\newcommand{\Os}{\mathcal{O}_{S,s}}
\newcommand{\lineb}{\c{L}}
\newcommand{\cyclm}{\Q(\sqrt[m]{1})}
\newcommand{\cyclmK}{K(\sqrt[m]{1})}
\newcommand{\LX}{L[X]}
\newcommand{\OS}{\mathcal{O}_S}
\newcommand{\bb}[1]{\textbf{#1}}
\newcommand{\OY}{\mathcal{O}_Y}
\newcommand{\glX}{\Gamma(X,\mathcal{O}_X)}
\newcommand{\glY}{\Gamma(Y,\mathcal{O}_Y)}
\newcommand{\finKX}{f\in K[X]}
\newcommand{\ser}[1]{\sm{n=0}{\infty}{#1}}
\newcommand{\sm}[3]{\underset{#1}{\overset{#2}{\sum}} #3}
\newcommand{\cl}[1]{\overline{#1}}
\newcommand{\sube}{\subseteq}
\newcommand{\hk}{\hookrightarrow}
\newcommand{\OYy}{\mathcal{O}_{Y,y}}
\newcommand{\supe}{\supseteq}
\newcommand{\resy}{\kappa(y)}
\newcommand{\LK}{L/K}
\newcommand{\iso}{\overset{\sim}{\to}}
\newcommand{\isom}[3]{#1\overset{#2}{\iso}#3}
\newcommand{\kn}{k^n}
\newcommand{\kvec}{\textbf{vect}(k)}
\newcommand{\fkvec}{\textbf{vect}_{<\infty}(k)}
\newcommand{\fz}{f(X)=0}
\newcommand{\KIsom}{L\underset{K}{\overset{\sim}{\to}} L}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\L}{\mathbb{L}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\A}{\mathbb{A}}
\newcommand{\P}{\mathbb{P}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Zp}{\mathbb{Z}_p}
\newcommand{\Qp}{\mathbb{Q}_p}
\newcommand{\Qq}{\mathbb{Q}_q}
\newcommand{\Fp}{\mathbb{F}_p}
\newcommand{\I}{[0,1]}
\newcommand{\In}{[0,1]^n}
\newcommand{\Fpn}{\mathbb{F}_{p^n}}
\newcommand{\Fpm}{\mathbb{F}_{p^m}}
\newcommand{\Zn}{\mathbb{Z}/{n\mathbb{Z}}}
\newcommand{\Zx}[1]{\mathbb{Z}/{#1\mathbb{Z}}}
\newcommand{\md}[3]{#1\equiv #2\pmod{#3}}
\newcommand{\ga}{\Gal(L/K)}
\newcommand{\aga}[1]{\Gal(\overline{#1}/#1)}
\newcommand{\sga}[1]{\Gal(#1^{sep}/{#1})}
\newcommand{\gal}[2]{\Gal(#1/{#2})}
\newcommand{\c}[1]{\mathcal{#1}}
\newcommand{\limes}[1]{\underset{i\in I}{\varprojlim{#1_i}}}
\newcommand{\Co}[2]{H^p(#1,#2)}
\newcommand{\OK}{\mathcal{O}_K}
\newcommand{\OL}{\mathcal{O}_L}
\newcommand{\res}[1]{\kappa(#1)}
\newcommand{\resx}{\kappa(x)}
\newcommand{\Te}{[T]}
\newcommand{\Tee}{[T_1,T_2]}
\newcommand{\Teee}{[T_1,T_2,T_3]}
\newcommand{\Ten}{[T_1\cos T_n]}
\newcommand{\Tem}{[T_1\cos T_m]}
\newcommand{\pts}{\cdots}
\newcommand{\pt}{\cdot}
\newcommand{\hm}[3]{\Hom_{#1}(#2,#3)}
\newcommand{\hom}[2]{\Hom(#1,#2)}
\newcommand{\dash}{\dashrightarrow}
\newcommand{\schemes}{\bb{(Sch)}}
\newcommand{\tx}[1]{\text{ #1 }}
\newcommand{\mm}{\ff{m}}
\newcommand{\arr}[3]{#1\overset{#2}{\to} #3}
\newcommand{\nrm}[1]{\left\|#1\right\|}
\newcommand{\nr}{\nrm{-}}
\newcommand{\ext}[2]{#1/{#2}}
\newcommand{\lam}{\lambda}
\newcommand{\a}{\alpha}
\newcommand{\be}{\beta}
\newcommand{\g}{\gamma}
\newcommand{\de}{\delta}
\newcommand{\vp}{\varphi}
\newcommand{\p}{\phi}
\newcommand{\bul}{\bullet}
\newcommand{\t}{\tau}
\newcommand{\s}{\sigma}
\newcommand{\ze}{\zeta}
\newcommand{\tm}{\times}
\newcommand{\tms}{\times\pts\times}
\newcommand{\ot}{\otimes}
\newcommand{\ots}{\otimes\pts\otimes}
\newcommand{\pls}{+\pts +}
\newcommand{\cos}{,\pts,}
\newcommand{\op}{\oplus}
\newcommand{\ops}{\oplus\pts\oplus}
\newcommand{\cr}{\circ}
\newcommand{\crs}{\circ\pts\circ}
\)
Hallo zusammen.
Ich verstehe folgende Definition nicht:
\(R\) ist ein vollständiger Ring.
Ich nehme mal ohne Beweis an, dass die implizite Behauptung \(\Omega^1_{R[[t]]/R}\cong R[[t]]dt\) richtig ist (was eigentlich nicht ganz trivial ist..).
Was ist \(\omega\)?
Was bedeutet \(\omega\circ F(S,T)\)?
Das ist von Haus aus erstmal nicht definiert.
Kann jemand das erklären?
\(\mathcal{F}\) ist eine eindimensionale Formale Gruppe und \(F(X,Y)\) die definierende Formale Potenzreihe.
Grüße
-----------------
"Jedes Gehirn kann Fragen beantworten. Es geht darum die richtigen Fragen zu finden."\(\endgroup\)
|
 Profil
 Quote
 Link |
|
Home
Wie unterstütze ich den Matheplaneten mit Geld?
Themenstart: 2018-12-06
[Neues Thema]