One place up close

Fields and curves read prime by prime: a field totally ramified over Q_p read through its unit's digits, the split primes of a quadratic field that are principal and where the first one sits, what the split primes of a cubic field carry in its class group, and which plane curves over a finite field hold every unit power of a torsion point.

• OBSERVATORY — what the digits of a ramified field read
• PRINCIPAL — where a quadratic field's first principal prime sits
• TRIPLE — what a cubic field's split primes carry
• TORSION — which torsion a curve holds, by monomials and by degree