From e3ed89039f036efa39e416b758a214070050c236 Mon Sep 17 00:00:00 2001 From: Robert Cardona Date: Sat, 21 Feb 2015 20:04:51 -0800 Subject: [PATCH] Fixed minor typos in chow.tex Capitalized Greek/Roman, "vectorbundle" to "vector bundle" and "succesive" to "successive". --- chow.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/chow.tex b/chow.tex index e0bd8016a..8b25035a1 100644 --- a/chow.tex +++ b/chow.tex @@ -1720,7 +1720,7 @@ \section{Periodic complexes} \medskip\noindent To shorten the formulas below we are going to write $\alpha x$ instead of $\alpha(x)$ in the following. No confusion should result since -all maps are indicated by greek letters and elements by roman letters. +all maps are indicated by Greek letters and elements by Roman letters. We are going to choose \begin{enumerate} \item an admissible sequence $z_1, \ldots, z_k \in K$ @@ -6576,7 +6576,7 @@ \section{Affine bundles} \begin{remark} \label{remark-when-isomorphism} We will see later (Lemma \ref{lemma-vectorbundle}) -that if $X$ is a vectorbundle over $Y$ then +that if $X$ is a vector bundle over $Y$ then the pullback map $A_k(Y) \to A_{k + r}(X)$ is an isomorphism. Is this true in general? \end{remark} @@ -7940,7 +7940,7 @@ \section{Degrees of zero cycles} Assume $X$ is a proper curve over $k$. By Divisors, Lemma \ref{divisors-lemma-filter-after-modification} there exists a modification $f : X' \to X$ such that $f^*\mathcal{E}$ -has a filtration whose succesive quotients are invertible +has a filtration whose successive quotients are invertible $\mathcal{O}_{X'}$-modules. Since $f_*[X']_1 = [X]_1$ we conclude from Lemma \ref{lemma-pushforward-cap-cj} that $$