Timeline for Relation between valuation of p-adic regulator of totally real field and its finite p-unramified abelian extensions

8 events

when toggle format	what		by	license	comment
May 24, 2017 at 17:03	comment	added	Barry		@FilippoAlbertoEdoardo Just got a copy of this book and indeed, you are right. The group he calls $\mathcal{T}_p^{\mathrm{ord}}$ is what I called $\Gamma$. In Chapter III, Remarks 2.6.5, Gras gives a formula for the order of $\Gamma$ in terms of the $p$-adic regulator of $K$ and other simple arithmetic quantities (assuming Leopoldt, so this order is finite). I think in the example I described, $\Gamma$ is cyclic, so knowing the order is the exponent. Thanks for the help.
May 23, 2017 at 22:33	comment	added	Filippo Alberto Edoardo		Have you looked in Gras' "Class Field Theory from theory to practice"? He introduces a module $Tor$ which might be precisely what you are looking for, but I don't have my copy at hand.
May 23, 2017 at 19:18	history	edited	Barry	CC BY-SA 3.0	added 42 characters in body
May 23, 2017 at 19:01	history	edited	Barry	CC BY-SA 3.0	edited body
May 23, 2017 at 18:56	history	edited	Barry	CC BY-SA 3.0	added 2496 characters in body
May 23, 2017 at 18:21	comment	added	Barry		Yes. See my edit for one case.
May 23, 2017 at 17:28	comment	added	KConrad		Do you have any numerical examples that suggest there might be a relationship between those objects?
May 23, 2017 at 16:33	history	asked	Barry	CC BY-SA 3.0