Timeline for Are Kato's zeta elements integral?
Current License: CC BY-SA 2.5
9 events
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| Nov 25, 2010 at 12:52 | comment | added | Olivier | @Chris I admit I never considered this question (of optimal versus minimal): I tend to work with the first étale cohomology group with coefficients in $\mathbb Z_{p}$ and forget about elliptic curves. | |
| Nov 25, 2010 at 10:46 | comment | added | Chris Wuthrich | The added remark on the $\mu$-invariant is very interesting. It would be worth trying to do that. Maybe in the end the minimal vs. optimal curve as in Steven's conjecture would again create a problem. | |
| Nov 24, 2010 at 22:40 | history | edited | Olivier | CC BY-SA 2.5 |
Answered OP questions in comments
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| Nov 24, 2010 at 17:13 | comment | added | David Loeffler | @Francois: The uniqueness of the stable lattice up to homothety is strictly weaker than assuming the surjectivity of the Galois rep; it is true as long as the mod p rep is irreducible. That is why I wondered if this weaker hypothesis was sufficient. | |
| Nov 24, 2010 at 16:58 | comment | added | François Brunault | @David. Kato uses hypothesis (12.5.2) to deduce that there is only 1 homothety class of Galois stable lattice in $V$. See paragraphs 13.14 and 14.7. However, I don't know whether this condition is really crucial, as you're asking. | |
| Nov 24, 2010 at 15:12 | comment | added | Chris Wuthrich | I fear I won't escape this one :-). I was hoping someone else would reply. The corrections are not complete and I have just taken them off my webpage, not to create more confusion. | |
| Nov 24, 2010 at 13:33 | comment | added | David Loeffler | I can't actually see anywhere in Kato's paper where the full force of his hypothesis (12.5.2) is used. Could you perhaps show me where to look? | |
| Nov 24, 2010 at 13:09 | comment | added | David Loeffler | Could you explain a little more about your last paragraph? The integrality of the Euler system clearly implies that the $\mu$-invariant is $\ge 0$, but it doesn't imply that it's 0, surely? | |
| Nov 24, 2010 at 12:54 | history | answered | Olivier | CC BY-SA 2.5 |