scheme of finite type造句

The latter come as function fields of schemes of finite type over integers and their appropriate localization and completions.
Assume that " X " is a normal integral separated scheme of finite type over a field.
The scheme need not be flat over, in this case it is a scheme of finite type over some.
If " X " is a scheme of finite type over a field there is a natural map from divisors to line bundles.
Then any smooth separated scheme of finite type over " k " is a finite disjoint union of smooth varieties over " k ".
It's difficult to find scheme of finite type in a sentence. 用scheme of finite type造句挺难的

In characteristic 0 a result of Cartier shows that all groups schemes of finite type are non-singular, so the dimension of their tangent space is their dimension.
Any complete group variety ( variety here meaning reduced and geometrically irreducible separated scheme of finite type over a field ) is automatically commutative, by an argument involving the action of conjugation on jet spaces of the identity.
If " X " is a scheme of finite type over " k ", one can glue the rigid dualizing complexes that its affine pieces have, and obtain a rigid dualizing complex R _ X.
Here X is a separated scheme of finite type over the finite field " F " with q elements, and Frob q is the geometric Frobenius acting on \ ell-adic 閠ale cohomology with compact supports of \ overline { X }, the lift of X to the algebraic closure of the field " F ".
Grothendieck's use of these universes ( whose existence cannot be proved in ZFC ) led to some uninformed speculation that 閠ale cohomology and its applications ( such as the proof of Fermat's last theorem ) needed axioms beyond ZFC . In practice 閠ale cohomology is used mainly for constructible sheaves over schemes of finite type over the integers, and this needs no deep axioms of set theory : with a little care it can be constructed in this case without using any uncountable sets, and this can easily be done in ZFC ( and even in much weaker theories ).