Cohen-Lenstra heuristics and the Spiegelungssatz; function fields |
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Authors: | Yoonjin Lee |
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Affiliation: | Department of Mathematics, Clark Science Center, Smith College, Northampton, MA 01063, USA |
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Abstract: | In this paper, we study the compatibility of Cohen-Lenstra heuristics with Leopoldt's Spiegelungssatz (= the reflection theorem) in the case of cyclic function fields. First, we prove a group-theoretical version of the Spiegelungssatz for cyclic function fields. Then we show the internal consistency of the function field analogue of Cohen-Lenstra heuristics in the case of cyclic function fields. It thus supports the validity of Cohen-Lenstra heuristics in function fields. |
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Keywords: | primary 11R29 secondary 11Sxx, 11Rxx |
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