Postdoc at the University of Bristol

Jun
15
awarded Nice Question
May
30
revised Endomorphism algebras of abelian surfaces with real multiplication
added 10 characters in body
May
30
awarded Curious
May
29
asked Endomorphism algebras of abelian surfaces with real multiplication
Jan
19
awarded Yearling
Jan
19
awarded Yearling
Nov
27
awarded Autobiographer
Nov
27
awarded Autobiographer
Nov
6
awarded Popular Question
Nov
6
awarded Necromancer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Sep
24
awarded Autobiographer
Jun
21
awarded Editor
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 :)
1 2 3 4 5