algebra, algebraic geometry, algebraic topology, manifolds, math, number theory, topology

Volumes of p-adic Schemes

I came across this idea a long time ago, but I needed the result that uses it in its proof again, so I was curious about figuring out what in the world is going on. It turns out that you can make "$latex {p}&fg=000000$-adic measures" to integrate against on algebraic varieties. This is a pretty… Continue reading Volumes of p-adic Schemes

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algebra, algebraic geometry, number theory

Brauer-Manin Obstruction

We will continue with the Brauer group after this post, but today let's answer the question: Why should we care about the Brauer group? We gave one good reason back when talking about rational surfaces. It provided something that might be computable to detect whether or not our variety had good reduction. Today let's consider… Continue reading Brauer-Manin Obstruction