Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $X$ a smooth projective geometrically connected curve over a finite field $k$. Let $J$ a smooth commutative group scheme over $X$ and $F$ the function field of $X$.

Do we have a formula to compute $H^{1}(k,J(\mathbb{A})/J(F))$ where $\mathbb{A}$ is the ring of adeles?

share|improve this question
I think you might be able to deal with such a cohomology group using global tate duality. Try for example the book "Cohomology of number fields" by Neukirch, Schmidt and Winberg. Note that despite the title, they do indeed study all global fields –  Daniel Loughran Jan 31 '13 at 18:14
This question looks like it may be incorrectly formulated: the Galois group of $k$ has no evident nontrivial action on $J(\mathbf{A})/J(F)$, so what could be interesting about this cohomology and more specifically: how would one find oneself confronted with wanting to know about it? –  user30180 Feb 3 '13 at 7:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.