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visits member for 4 years, 6 months
seen Jul 17 at 10:09

Postdoc at the University of Copenhagen


Jun
5
comment A pointless circle in HoTT
What is your definition of "inhabited by"?
Jun
4
comment Source of quotation about the waste-baskets of physicists
Well to have been more accurately (R.I.P.)
May
5
comment Is GL2( R ) - > PGL2( R ) surjective?
In general the map will be surjective when Pic(R) is trivial. Brian Conrad's homework on group schemes walks you through this to a certain extent. If R as a Dedekind domain you can think of the elements of $PGL_n(R)$ as being pseudomatrices of fractional ideals all of whose $n$-fold products which go into the determinant are principal. If the class group is trivial, then all the entries have to be principal anyway and you're left with a standard matrix in $GL_n(R)$ up to unit multiple in $R$.
Apr
24
comment Spicing up Riemann surfaces course (revised)
What's so bland about Riemann Surfaces that requires spicing up?
Apr
12
answered Quadratic twist of an elliptic curve given by non-Weierstrass model
Apr
10
comment Canonical lifts from $\mathbb F_q$ and CM-theory
I have two references in mind: 1) Messing's book shows how if $A_{/k}$ is an ordinary abelian variety then the Serre-Tate Canonical lift $\mathcal{A}_{W(k)}$ admits an isomorphism $End_k(A) \cong End_{W(k)}(\mathcal{A})$. 2) Deligne's Inventiones paper "Varieties Abeliennes Ordinaires..." shows how the choice of embedding $W(k) \hookrightarrow \mathbf{C}$ doesn't change anything. He therefore shows an equivalence of categories between ordinary abelian varieties over a finite field vs $\mathbf{C}$ whose details escape me at the moment but the paper is 3 pages so you should read it anyway :)
Apr
1
comment Etale covers of a hyperelliptic curve
You're right. I still think there's a way to say that if $Y$ was also Galois then there's a way to break it up into a composite cover with $X$ in the middle but I don't really have any evidence for that.
Apr
1
revised Etale covers of a hyperelliptic curve
edit: removed previous edit
Apr
1
revised Etale covers of a hyperelliptic curve
added 273 characters in body
Apr
1
answered Etale covers of a hyperelliptic curve
Mar
12
comment Connections between Riemann hypothesis for curves over finite fields and Ramanujan property for graphs
For Ramanujan graphs coming Cayley graphs I don't know the exact story, but using Brandt matrices you can get Ramanujan graphs out of the dual graphs of certain Shimura curves. Pete Clark has some "rambling notes" on this subject here math.uga.edu/~pete/ramanujanrevisited.pdf and I covered some smaller cases in a course I taught a year ago.
Jan
27
awarded  Necromancer
Jan
19
awarded  Yearling
Dec
20
awarded  Revival
Dec
17
comment divisibility of Tamagawa numbers
Thank you, that was very silly of me. Explicitly, Reichert's paper on torsion structures over quadratic fields gives an example with p= 13.
Dec
17
comment divisibility of Tamagawa numbers
A number of people commented that there is a counterexample for $p=5$, which is of course not quite what you're asking about. I'll just note that the Tamagawa number of an elliptic curve over a dvf is essentially the valuation of the minimal discriminant (and thus $\le 12$) if it has split multiplicative reduction and something else (not a large prime) otherwise. So we're really talking about $p=11$ on the nose here and having sage search through (some fraction of) the Cremona database didn't find anything with tamagawa number divisible by 11.
Dec
15
comment What is $p$-adic Fourier series?
See page 50 of Koblitz's intro to $p$-adic numbers, $p$-adic analytis and zeta functions.
Dec
14
comment How can an extremely mathematically talented young person be helped to fulfill his/her potential?
I have no personal experience, but something that I've heard repeatedly is NOT to push the child through the normal curriculum as quickly as possible. If someone is interested in math, there's a lot that you can learn before getting to calculus. Teach the child the rest of math and they will have a much more robust background by the time they get past calculus. As a nice side effect, they will get to have some semblance of a normal social life if they aren't being rushed through different grades.
Dec
5
awarded  nt.number-theory
Dec
4
answered Isogeny classes and elliptic curves over finite fields