bio | website | perso.ens-lyon.fr/… |
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location | Lyon, France | |
age | 38 | |
visits | member for | 4 years, 11 months |
seen | Mar 21 at 12:28 | |
stats | profile views | 3,093 |
I am a number theorist working in Lyon (France).
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 |
comment |
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 |
comment |
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 |
Apr 4 |
asked | A criterion for freeness over a local ring |
Mar 27 |
answered | Galois descent for semilinear endomorphisms |
Jan 25 |
awarded | Nice Answer |
Dec 23 |
answered | Describing the ratio of uniformizers in B_dR |
Dec 17 |
comment |
Commuting invariants and duals of C_p vector spaces
Concerning your first question: a $G_K$-equivariant map from V to $C_p$ exists, for example, whenever $V$ is of Hodge-Tate type with one weight equal to $0$. This happens for lots of repns for which $V^{G_K} = 0$. |
Dec 4 |
comment |
Algebraic maximal extension and algebraic closure
$\mathbf{C}_p$ has plenty of immediate extensions, that is extensions that have the same value group and the same residue field. The compositum of all these is its spherical completion. Now lots of intermediate fields between $\mathbf{C}_p$ and its spherical completion would not be algebraic maximal. |