custom list numbering

trees/sga1/sga1-i/sga1-i.10.tree

@@ -83,18 +83,16 @@
     Then
   }
 
-  \todo{the following list should be i, ii, etc}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{i.}{
       #{K} is unramified over #{Y}.
     }
 
-    \li{
+    \lic{ii.}{
       If #{L} is an extension of #{K} that is unramified over #{Y}, and if #{Y'} is a normal prescheme, of field #{L}, that dominates #{Y} (e.g. the normalisation of #{Y} in #{L}), and #{M} an extension of #{L} that is unramified over #{Y'}, then #{M/K} is unramified over #{X} (this is the \em{transitivity} property).
     }
 
-    \li{
+    \lic{iii.}{
       Let #{Y'} be a normal integral prescheme that dominates #{Y}, of field #{K'/K};
       if #{L} is an extension of #{K} that is unramified over #{Y}, then #{L\otimes_K K'} is an extension of #{K'} that is unramified over #{Y'} (this is the \em{translation} property).
     }

trees/sga1/sga1-i/sga1-i.11.tree

@@ -11,12 +11,8 @@
   Here are two examples of this fact.
 }
 
-\p{
-  \todo{the following list should be a, b}
-}
-
-\ol{
-  \li{
+\olc{
+  \lic{a.}{
     Let #{C} be an algebraic curve with an ordinary double point #{x}, and let #{C'} be its normalisation, with #{a} and #{b} the two points of #{C'} over #{x}.
     Let #{C'_1} and #{C'_2} be copies of #{C'}, with #{a_i} (resp. #{b_i}) the point of #{C'_i} corresponding to #{a} (resp. #{b}).
     In the curve #{C'_1\coprod C'_2}, we identify #{a_1} with #{b_2}, and #{a_2} with #{b_1} (we leave making this process of identification precise to the reader; it will be explained in Chapter VI of the multiplodoque, but, in the case of curves over an algebraically closed field, is already covered in Serre's book on algebraic curves).
@@ -27,7 +23,7 @@
     We note that is was questions of this sort that gave birth to the "theory of descent" for schemes.
   }
 
-  \li{
+  \lic{b.}{
     \p{
       Let #{A} be a complete integral local ring;
       we know that its normalisation #{A'} is finite over #{A} (by Nagata), and is thus a complete semi-local ring, and thus local, since it is integral.

trees/sga1/sga1-i/sga1-i.2.tree

@@ -15,16 +15,14 @@
     Then the following conditions are equivalent:
   }
 
-  \p{\todo{the following list should be i, ii, etc}}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{i.}{
       #{B/\mathfrak{m}B} is of finite dimension over #{k=A/\mathfrak{m}}.
     }
-    \li{
+    \lic{ii.}{
       #{\mathfrak{m}B} is an ideal of definition, and #{B/\mathfrak{r}(B)=k(B)} is an extension of #{k=k(A)}.
     }
-    \li{
+    \lic{iii.}{
       The completion #{\widehat{B}} of #{B} is finite over the completion #{\widehat{A}} of #{A}.
     }
   }

trees/sga1/sga1-i/sga1-i.3.tree

@@ -15,16 +15,14 @@
     Then the following conditions are equivalent:
   }
 
-  \p{\todo{the following list should be i, ii, etc}}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{i.}{
       #{\sh{O}_x/\mathfrak{m}_y\sh{O}_x} is a finite separable extension of #{k(y)}.
     }
-    \li{
+    \lic{ii.}{
       #{\Omega_{X/Y}^1} is zero at #{x}.
     }
-    \li{
+    \lic{iii.}{
       The diagonal morphism #{\Delta_{X/Y}} is an open immersion on a neighbourhood of #{x}.
     }
   }
@@ -45,14 +43,12 @@
   \number{I.3.2}
   \taxon{definition}
 
-  \p{\todo{the following list should be a, b}}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{a.}{
       Let #{f} satisfy one of the equivalent conditions of \ref{sga1-i.3.1}.
       Then we say that #{f} is \em{unramified} at #{x}, or that #{X} is unramified at #{x} on #{Y}.
     }
-    \li{
+    \lic{b.}{
       Let #{A\to B} be a local homomorphism.
       We say that it is \em{unramified}, or that #{B} is a local \em{unramified} algebra on #{A}, if #{B/\mathfrak{r}(A)B} is a finite separable extension of #{A/\mathfrak{r}(A)}, i.e. if #{\mathfrak{r}(A)B=\mathfrak{r}(B)} and #{k(B)} is a separable extension of #{k(A)}.
       (cf. regrets in [III 1.2])
@@ -99,16 +95,14 @@
   \number{I.3.5}
   \taxon{proposition}
 
-  \p{\todo{the following list should be i, ii, etc}}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{i.}{
       An immersion is ramified.
     }
-    \li{
+    \lic{ii.}{
       The composition of two ramified morphisms is also ramified.
     }
-    \li{
+    \lic{iii.}{
       Base extension of a ramified morphisms is also ramified.
     }
   }
@@ -125,16 +119,14 @@
   \number{I.3.6}
   \taxon{corollary}
 
-  \p{\todo{the following list should be iv, v, etc}}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{iv.}{
       The cartesian product of two unramified morphisms is unramified.
     }
-    \li{
+    \lic{v.}{
       If #{gf} is unramified then so too is #{f}.
     }
-    \li{
+    \lic{vi.}{
       If #{f} is unramified then so too is #{f_\mathrm{red}}.
     }
   }

trees/sga1/sga1-i/sga1-i.4.tree

@@ -6,8 +6,6 @@
 \import{sga1-macros}
 \put\transclude/numbered{false}
 
-\todo{fix the auto-capitalisation of the title not recognising É}
-
 \p{
   We are going to suppose that everything concerning flat morphisms that we need to be true is indeed true;
   these facts will be proved later, if there is time.
@@ -18,16 +16,14 @@
   \taxon{definition}
   \number{I.4.1}
 
-  \todo{this list should be a, b}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{a.}{
       Let #{f\colon X\to Y} be a morphism of finite type.
       We say that #{f} is \em{étale} at #{x} if #{f} is both flat and unramified at #{x}.
       We say that #{f} is étale if it is étale at all points.
       We say that #{X} is étale at #{x} over #{Y}, or that it is a #{Y}-prescheme which is étale at #{x} etc.
     }
-    \li{
+    \lic{b.}{
       Let #{f\colon A\to B} be a local homomorphism.
       We say that #{f} is étale, or that #{B} is étale over #{A}, if #{B} is flat and unramified over #{A}
       \footnote{cf. regrets in \fref{sga1-iii.1.2}.}
@@ -98,16 +94,14 @@
   \taxon{proposition}
   \number{I.4.6}
 
-  \todo{this list should be i, ii etc}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{i.}{
       An open immersion is étale.
     }
-    \li{
+    \lic{ii.}{
       The composition of two étale morphisms is étale.
     }
-    \li{
+    \lic{iii.}{
       The base extension of an étale morphism is étale.
     }
   }

trees/sga1/sga1-i/sga1-i.9.tree

@@ -115,13 +115,11 @@
     Let #{f\colon A\to B} be a local homomorphism, with #{B} isomorphic to the localisation of an #{A}-algebra of finite type over #{A}.
   }
 
-  \p{\todo{the following list should be i, ii}}
-
-  \ol{
-    \li{
+  \olc{
+    \lic{i.}{
       If #{f} is étale, then #{A} is normal if and only if #{B} is normal.
     }
-    \li{
+    \lic{ii.}{
       If #{A} is normal, then #{f} is étale if and only if #{f} is injective and unramified (and then #{B} is normal, by (i)).
     }
   }
@@ -146,13 +144,11 @@
   \subtree[sga1-i.9-serres-criterion]{
     \title{Serre's criterion}
 
-    \p{\todo{the following list should be i, ii}}
-
-    \ol{
-      \li{
+    \olc{
+      \lic{i.}{
         For every rank-#{1} prime ideal #{\mathfrak{p}} of #{A}, #{A_\mathfrak{p}} is normal (or, equivalently, regular);
       }
-      \li{
+      \lic{ii.}{
         For every rank-#{\geq2} prime ideal #{\mathfrak{p}} of #{A}, the depth of #{A_\mathfrak{p}} is #{\geq2}.
         \footnote{cf. EGA IV 5.8.6.}
       }

trees/sga1/sga1-macros.tree

@@ -1,3 +1,12 @@
+\xmlns:html{http://www.w3.org/1999/xhtml}
+
+\def\olc[body]{
+ \<html:ol>{\body}
+}
+\def\lic[lbl][body]{
+ \<html:li>[style]{list-style-type: "\lbl "}{\body}
+}
+
 \def\tr{#{\operatorname{tr}}}
 \def\Spec{#{\operatorname{Spec}}}
 \def\Hom{#{\operatorname{Hom}}}

trees/sga6/sga6-0/sga6-0.1.tree

@@ -9,12 +9,17 @@
   Recall the Riemann–Roch formula for a proper morphism
   ##{f\colon X\to Y}
   of smooth quasi-projective schemes over a field #{k} and a coherent sheaf #{\sh{F}} on #{X}:
-  \todo{equation numbering}
-  ##{
-    \Todd(T_Y)\ch_Y(f_*(\cl(\sh{F})))
-    = f_*(\Todd(T_X)\ch_X(\sh{F}))
-  \startverb\tag{1.1}\stopverb
+
+  \subtree[sga6-0.1-equation-1.1]{
+    \taxon{equation}
+    \number{1.1}
+    ##{
+      \Todd(T_Y)\ch_Y(f_*(\cl(\sh{F})))
+      = f_*(\Todd(T_X)\ch_X(\sh{F}))
+    \startverb\tag{1.1}\stopverb
+    }
   }
+
   where #{\cl(\sh{F})} denotes the class of #{\sh{F}} in the group #{K(X)} of classes of coherent sheaves on #{X}, and #{\ch_X} and #{\ch_Y} denote the Chern characters of on #{X} and #{Y} (resp.), and #{T_X} and #{T_Y} the tangent bundles to #{X} and #{Y} (resp.).
   This formula holds in #{A(Y)\otimes_\ZZ\QQ}, where #{A(Y)} is the Chow ring of #{Y};
   the #{f_*} on the right-hand side is induced by tensoring with #{\QQ} the "direct image of cycles" homomorphism
@@ -28,18 +33,29 @@
   }
   As we know, #{\Todd(-)} and #{\ch(-)} are universal polynomials in the Chern classes of the argument with coefficients in #{\QQ}.
   Since the constant term of #{\Todd(-)} is #{1}, it is an invertible element for any value of the argument, so that Equation (1.1) can be rewritten, after multiplication by #{\Todd(T_Y)^{-1}}, in the form which is more useful for our needs:
-  \todo{equation numbering}
-  ##{
-    \ch_Y(f_*(\cl(\sh{F})))
-    = f_*(\Todd(T_f)\ch_X(\sh{F}))
-  \startverb\tag{1.2}\stopverb
+
+  \subtree[sga6-0.1-equation-1.2]{
+    \taxon{equation}
+    \number{1.2}
+    ##{
+      \ch_Y(f_*(\cl(\sh{F})))
+      = f_*(\Todd(T_f)\ch_X(\sh{F}))
+    \startverb\tag{1.2}\stopverb
+    }
   }
+
   where we set
-  ##{
-    T_f
-    = T_X - f^*(T_Y) \in K(X)
-  \startverb\tag{1.3}\stopverb
+
+  \subtree[sga6-0.1-equation-1.3]{
+    \taxon{equation}
+    \number{1.3}
+    ##{
+      T_f
+      = T_X - f^*(T_Y) \in K(X)
+    \startverb\tag{1.3}\stopverb
+    }
   }
+
   so that #{T_f} plays the role of a \em{virtual relative tangent bundle} of #{X} over #{Y}.
   In the case where the morphism #{f} is smooth (i.e. with everywhere-surjective tangent map), we have simply
   ##{
@@ -58,13 +74,11 @@
   One of the main goals of this Seminar is to generalise Equation (1.2) simultaneously in two directions:
 }
 
-\todo{this list should be a, b}
-
-\ol{
-  \li{
+\olc{
+  \lic{a.}{
     Remove the hypothesis of the existence of a base field #{k}.
   }
-  \li{
+  \lic{b.}{
     Replace the regularity hypotheses on #{Y} and #{X} by a "local regularity" hypothesis on #{f}.
   }
 }
@@ -73,10 +87,8 @@
   Finally, along the way, we will equally deal with the problem:
 }
 
-\todo{this list should be c}
-
-\ol{
-  \li{
+\olc{
+  \lic{c.}{
     Remove the quasi-projectivity hypotheses which, in the absence of a base field, are expressed by the existence of ample invertible modules on #{X} and on #{Y}.
   }
 }

trees/sga6/sga6-i/sga6-i.0.tree

@@ -81,13 +81,11 @@
   this theorem is, in reality, a conjecture, but has nevertheless been proven in the two particular following cases:
 }
 
-\p{\todo{the following list should be a, b}}
-
-\ol{
-  \li{
+\olc{
+  \lic{a.}{
     #{S} is locally Noetherian;
   }
-  \li{
+  \lic{b.}{
     #{f} is projective.
   }
 }

trees/sga6/sga6-macros.tree

@@ -1,3 +1,12 @@
+\xmlns:html{http://www.w3.org/1999/xhtml}
+
+\def\olc[body]{
+ \<html:ol>{\body}
+}
+\def\lic[lbl][body]{
+ \<html:li>[style]{list-style-type: "\lbl "}{\body}
+}
+
 \def\proof[body]{
   \scope{
     \put\transclude/toc{false}