Talk:Exalcomm

Todo

• define morphisms between them
• give examples of morphisms and non-isomorphic extensions
• show module structure for exal
• define exal for schemes
• add explanation of composition of exal groups with the module formed by a direct sum of dual numbers, giving $H^{1}(X,T_{X})\oplus H^{1}(X,T_{X})$

Confusion in section "Relation with the cotangent complex"

I think there is a mistake here. The correct statement should be

$Exalcom_{A}(B,M)\cong Ext_{B}^{1}(L_{B/A},M)$.

Illusie, in [1], uses $Exal$ instead of Grothendieck's $Exalcom$.

None of the original French texts use $Exalcomm$, they write $Exalcom$ (EGA IV) or $Exal$ (Illusie).

Amyekut (talk) 10:32, 11 March 2023 (UTC)