Johnson-Leung
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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!