Timeline for Line bundles trivial after extension of the base-field
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Jan 17, 2010 at 21:59 | comment | added | Philipp Hartwig | David, this is a really great answer, thanks a lot for this beautiful example (I'm the one who asked this question before I had a real account here). | |
| Dec 11, 2009 at 4:03 | history | edited | David E Speyer | CC BY-SA 2.5 |
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| Dec 9, 2009 at 22:09 | comment | added | Evgeny Shinder | In particualar, when $K[X]^* = K^*$, the kernel is zero by Hilbert 90. | |
| Dec 9, 2009 at 22:08 | comment | added | Evgeny Shinder | In the case of Galois extension K/k one can explicitly describe the kernel of $Pic(X) \to Pic(X_K)$. I believe it's equal to $H^1(G, K[X]^*)$. It is a part of 5-term exact sequence coming from a Hochshild-Serre spectral sequence, associated to Galois covering $X_K \to X$. | |
| Dec 9, 2009 at 19:03 | comment | added | Pete L. Clark | This is a nice answer. (I previously had answered the question incorrectly, and with no justification.) In the case of curves (as above), it is related to an exact sequence of Mike Rosen: see equation (2) on p. 6 of math.uga.edu/~pete/ellipticded.pdf | |
| Dec 9, 2009 at 18:51 | history | answered | David E Speyer | CC BY-SA 2.5 |