The Stacks project

Comments 801 to 820 out of 9050 in reverse chronological order.

\begin{equation*} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation*}

On left comment #8912 on Lemma 10.47.14 in Commutative Algebra

Because then the residue field is a quotient of the ring, whence integral over (because and are integral over ), whence algebraic extension of containing .


On left comment #8911 on Section 35.13 in Descent

Thanks for pointing out this very confusing typo. Fixed here.


On left comment #8910 on Lemma 15.23.12 in More on Algebra

Thanks and fixed here.


On left comment #8909 on Section 12.26 in Homological Algebra

Can't find it.


On left comment #8908 on Lemma 33.9.3 in Varieties

Thanks and fixed here.


On left comment #8907 on Lemma 50.15.7 in de Rham Cohomology

Thanks and fixed here.


On left comment #8906 on Lemma 59.29.9 in Étale Cohomology

Thanks and fixed here.


On left comment #8905 on Lemma 20.11.1 in Cohomology of Sheaves

Thanks and fixed here.


On left comment #8904 on Lemma 5.8.16 in Topology

@#8892 I mean the new edition of EGA I published by Springer in 1971, Chapter 0, Proposition (2.9.2), p. 68. The statement that is a bijection between open sets of and is in the same page, (2.9.2.5).


On left comment #8903 on Lemma 30.6.1 in Cohomology of Schemes

Thanks! The proof was a little to sketchy so I added some clarifications as well. See changes.


On left comment #8902 on Lemma 70.15.1 in Limits of Algebraic Spaces

Thanks and fixed here.


On left comment #8901 on Section 110.34 in Examples

Thanks and fixed here.


On left comment #8900 on Lemma 42.2.4 in Chow Homology and Chern Classes

Thanks! The statement is correct but the proof was not. Now fixed here.


On left comment #8899 on Lemma 36.4.5 in Derived Categories of Schemes

Thanks and fixed here.


On left comment #8898 on Lemma 13.18.9 in Derived Categories

Thanks and fixed here.


On left comment #8897 on Definition 59.18.1 in Étale Cohomology

Thanks and fixed here.


On left comment #8896 on Section 91.2 in Deformation Theory

Thanks and fixed here.


On left comment #8895 on Lemma 10.168.4 in Commutative Algebra

Thanks and fixed here.


On left comment #8894 on Lemma 29.36.18 in Morphisms of Schemes

Good idea. Implemented here.


On left comment #8893 on Lemma 10.53.4 in Commutative Algebra

Add a few words here.