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Jun
17 |
awarded | Popular Question |
Sep
28 |
accepted | Explicit period lattices for abelian surfaces |
Sep
28 |
awarded | Commentator |
Sep
28 |
comment |
Explicit period lattices for abelian surfaces
OK. I edited it to not imply that I have a projective model. Formally applying Weil restriction, I get the surface as the intersection of two affine varieties. |
Sep
28 |
revised |
Explicit period lattices for abelian surfaces
deleted 8 characters in body |
Sep
28 |
comment |
Explicit period lattices for abelian surfaces
This is explicit: The Weil restriction of an elliptic curve over a quadratic extension is an abelian surface. Restriction of scalars of the ideal of the curve gives two equations in four variables. I'm not an algebraic geometer, but I think that makes it a complete intersection. |
Sep
27 |
asked | Explicit period lattices for abelian surfaces |
May
2 |
awarded | Good Answer |
Jan
5 |
awarded | Yearling |
Sep
14 |
awarded | Enthusiast |
Sep
8 |
comment |
an engineering Ph.D. teaching math in college
Just saw your comment, Keith. I guess you already knew all of these things. I do think that a phone call beats an email for getting in touch with potential employers. Anyway, good luck to your friend! |
Sep
8 |
answered | an engineering Ph.D. teaching math in college |
Jun
18 |
awarded | Autobiographer |
Jun
18 |
comment |
What should be learned in a first serious schemes course?
For me, it was another one of those things that is easy once you understand what is going on, but very easy to screw up before that! |
Jun
18 |
comment |
What should be learned in a first serious schemes course?
Well, I think that I'll elaborate with an example. If $X=$Spec$F$ is a variety over $\mathbb{Q}$ and $F$ is a number field then $H^0_B(X(\mathbb{C}),\mathbb{Q})$ is isomorphic to the group ring $\mathbb Q[G]$ where $G$ is the Galois group of $F$ over $\mathbb{Q|$. If I would like to decompose this into the irreducible representations of $\mathbb{Q}$, then I need to extend \em{coefficients} to a field $E$ over which the idempotents are defined. So I would be looking at $H^0_B(X(\mathbb{C}),E)$. If I wanted to look at a subgroup of $G$, I would need to change the base. |
Jun
18 |
answered | What should be learned in a first serious schemes course? |
Apr
2 |
awarded | Critic |
Mar
11 |
comment |
Does the image of a p-adic Galois representation always lie in a finite extension?
This is the line of argument that I was attempting to make, but I accepted jnewton's answer because it came in first. I wanted to let you know that in your write-up you switch from $K_r$ to $G_r$ midway through the proof. Thanks again! |
Mar
11 |
awarded | Nice Question |
Mar
11 |
comment |
Does the image of a p-adic Galois representation always lie in a finite extension?
It seemed to me that it must be true and well-known, since basic results do not appear to hold otherwise (for example, the existence of a G-stable lattice in V). The ring of integers of $\bar{\mathbb Q}_p$ is not very nice! |