Modular Units on Tate Curves
The generic units (which are algebraic functions of j) can be specialized whenever j is specialized, say into a number field. Three cases arise: when j is not integral, when j is integral without complex multiplication, and when j is integral with complex multiplication. The first case will be discussed in this chapter. The third case is in some sense the oldest and will be discussed later. The middle case is the one about which the least is known. A recent result of Harris [Har] gives an asymptotic estimate for the rank of the specialized units.
KeywordsLocal Ring Galois Group Number Field Prime Divisor Integral Closure
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