Adele groups , p - adic groups , solenoids
نویسنده
چکیده
1. Hensel’s lemma 2. Metric definition of p-adic integers Zp and p-adic rationals Qp 3. Elementary/clumsy definitions of adeles A and ideles J 4. Uniqueness of objects characterized by mapping properties 5. Existence of limits 6. Zp and Ẑ as limits 7. Qp and A as colimits 8. Abelian solenoids (R×Qp)/Z[1/p] and A/Q 9. Non-abelian solenoids and SL2(Q)\SL2(A) Although we will also give the more typical descriptions, we also show that the adeles A, p-adic integers Zp, p-adic rationals Qp, and related objects are already right under our noses, if only we can see them. These things are not artificial or mere stylistic choices. It is unwise to ignore them.
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