Timeline for Jacobians defined over smaller fields
Current License: CC BY-SA 3.0
4 events
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| Nov 5, 2012 at 11:37 | comment | added | user27056 | @Pete Clark: The definition of PHS given in those notes (in the 2nd sentence of the definition of WC-groups there) is incorrect over every field of positive characteristic. For example, it doesn't detect the effect of making $A$ act on a PHS for an abelian variety $A'$ through composition with a purely inseparable isogeny $A \rightarrow A'$ that isn't an isomorphism. Also, I disagree with the first sentence of section 2 of those notes (if one reflects on how the degree-1 cohomology of $A$ comes up in practice), though the two questions you raise there are reasonable nonetheless. | |
| Nov 5, 2012 at 8:00 | comment | added | Pete L. Clark | $\S 5$ of math.uga.edu/~pete/wcnotes.pdf contains an arguably more elementary proof that $H^1(K,B)$ contains infinitely many elements of order $n$ for any $n > 1$ (in fact over a more general class of fields). | |
| Oct 7, 2012 at 6:38 | history | edited | user27056 | CC BY-SA 3.0 |
added 20 characters in body
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| Oct 7, 2012 at 4:32 | history | answered | user27056 | CC BY-SA 3.0 |