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6 votes
0 answers
465 views

Torsionfree crystalline cohomology implies torsionfree etale cohomology?

Let $X$ be a smooth projective variety over an algebraically closed field $k$ of characteristic $p>0$. Let $W=W(k)$ be the ring of Witt vectors of $k$. Assume that the crystalline cohomology $H^2_{...
Monsie's user avatar
  • 91
4 votes
1 answer
272 views

How do non-trivial global differentials give non-trivial cohomology classes in positive characteristic

Let $k$ be an algebraically closed field and let $X$ be an $n$-dimensional smooth projective variety over $k$. If $k= \mathbb C$, there is a natural injective morphism of vector spaces $$H^0(X,\...
Carl's user avatar
  • 49