3
$\begingroup$

Given two schemes $X, Y$ with a map $f: X \rightarrow Y$, one should have a map $df: T^*Y \times_Y X \rightarrow T^*X$. How is this map defined (using the language of algebraic geometry, rather than the language of manifolds)?

  • 2
    One doesn't usually have a cotangent *bundle* so much as a cotangent *sheaf*, in which case it is not appropriate to use fibre product notation for pullback.2012-12-18
  • 1
    And the cotangent sheaves are relative some basis.2012-12-18

1 Answers 1