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fix \tag
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tim-at-topos committed Mar 24, 2024
1 parent 4c7a751 commit b965f30
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions trees/sga6/sga6-0/sga6-0.1.tree
Original file line number Diff line number Diff line change
Expand Up @@ -13,7 +13,7 @@
##{
\Todd(T_Y)\ch_Y(f_*(\cl(\sh{F})))
= f_*(\Todd(T_X)\ch_X(\sh{F}))
\tag{1.1}
\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};
Expand All @@ -32,13 +32,13 @@
##{
\ch_Y(f_*(\cl(\sh{F})))
= f_*(\Todd(T_f)\ch_X(\sh{F}))
\tag{1.2}
\startverb\tag{1.2}\stopverb
}
where we set
##{
T_f
= T_X - f^*(T_Y) \in K(X)
\tag{1.3}
\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
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