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Aug
2 |
answered | Generalization of Kummer isomorphism? |
Jul
31 |
awarded | Nice Answer |
Jul
30 |
awarded | Popular Question |
Jul
25 |
answered | Research-level mathematical bookstores |
Jul
9 |
comment |
Cyclotomic extension of p-adic fields
Oh ok, thank you for the clarification! |
Jul
9 |
comment |
Cyclotomic extension of p-adic fields
@Larsson: "Typical"? :-( See math.u-psud.fr/~biblio/pub/2000/abs/ppo2000_24.html for the preprint version of Fontaine's paper, and see mathoverflow.net/questions/96257/… concerning the availability of Asterisque. |
Jul
8 |
comment |
Cyclotomic extension of p-adic fields
What do you mean "what can be said"? If you add the $p^n$-th roots of $1$ for all $n$, (and not just the $p$-th roots as in your question) you get an extension whose Galois group is an open subgroup of $Z_p^\times$, and whose residue field is a finite extension of $F_p$. These extensions are used a lot in $p$-adic Hodge theory, so I suggest you look at papers in that area, eg Fontaine's "Arithmétique des représentations galoisiennes $p$-adiques". There's a lot of info about the ramification of that extension, for example. |
Jul
5 |
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Does there exist a non-square number which is the quadratic residue of every prime?
On the other hand, 16 is an 8th power modulo every prime! |
Jul
4 |
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Omitting primes from a Hecke algebra
@Kevin: "So knowing a Galois representation mod 2 does not tell you what the crystalline Frobenius eigenvalues are mod 2". I'm not sure exactly what you mean, but if ell=p, then the mod p Galois repn carries very little information about the Galois repn and the crystalline Frobenius. |
Jun
25 |
awarded | nt.number-theory |
Jun
25 |
awarded | Pundit |
Jun
24 |
comment |
Is there a known example of a curve X of genus > 1 over Q such that we know the number of points of X over the n-th cyclotomic field, for every n?
Concerning solvable points on projective curves: there are some results of Ciperiani and Wiles "Solvable points on genus one curves" and of Pal as well "Solvable points on projective algebraic curves", "Solvable points on genus one curves over local fields" and "Curves which do not become semi-stable after any solvable extension". |
Jun
7 |
comment |
Roadmap to reach Arithmetic Geometry for a Physics Major
Take a look at the book "From Number Theory to Physics". Exerpt from the blurb : "The 14 chapters of this book are extended, self-contained versions of expository lecture courses given at a school on "Number Theory and Physics" held at Les Houches for mathematicians and physicists. Most go as far as recent developments in the field. Some adapt an original pedagogical viewpoint." |
Jun
5 |
awarded | Citizen Patrol |
Jun
5 |
answered | Where to look for corrections of papers? |
May
24 |
awarded | Enlightened |
May
24 |
awarded | Nice Answer |
Apr
30 |
awarded | Yearling |
Apr
4 |
comment |
A criterion for freeness over a local ring
Great, thank you! |
Apr
4 |
accepted | A criterion for freeness over a local ring |