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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.
Nov
23
comment I know that you know…
There is a (not serious) mention of this in "A canticle for Leibowitz", but sadly I don't remember where exactly. Can somebody find the exact quotation?
Nov
21
answered Fastest way to factor integers < 2^60