A PRO-l VERSION OF THE CONGRUENCE SUBGROUP PROBLEM FOR MAPPING CLASS GROUPS OF GENUS ONE
نویسندگان
چکیده
Let l be a prime number. In the present paper, we discuss a pro-l version of the congruence subgroup problem for mapping class groups of genus one. Our main result is that the pro-2 version has an affirmative answer, but the pro-l version for l ≥ 11 has a negative answer. In order to give a negative answer to the problem in the case where l ≥ 11, we also consider the issue of whether or not the image of the natural outer action of the absolute Galois group of a certain number field on the geometric pro-l fundamental group of a modular curve is a pro-l group.
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