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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.

5 votes
Accepted

Tangent space of a finite flat group scheme

This is correct. Here's another to see it (assume for simplicity we are working over a field $k$). Let $R_\epsilon : = k[\epsilon]/\epsilon^2$ and let $S_\epsilon:= Spec R_\epsilon.$ This is a scheme …
Dmitry Vaintrob's user avatar
13 votes
Accepted

Can we use formal groups to recover Lie-theoretic representation theory in characteristic p?

The short answer is that the characteristic $p$ picture genuinely has more depth. In particular it's not correct to think of formal groups as "better" than Lie groups. In fact, they can be put on equa …
Dmitry Vaintrob's user avatar