<紀要論文>
QUANDLES ASSOCIATED TO GALOIS COVERS OF ARITHMETIC SCHEMES

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概要 Let X be a normal, separated and integral scheme of finite type over Z and M a set of closed points of X. To a Galois cover X^^˜ of X unramified over M, we associate a quandle whose underlying set con...sists of points of X^^˜ lying over M. As the limit of such quandles over all étale Galois covers and all étale abelian covers, we define topological quandles Q(X, M) and Q^<ab>(X, M), respectively. Then we study the problem of reconstruction. Let K be Q or a quadratic field, OK its ring of integers, X = Spec O_K \{p} the complement of a closed point such that π_1(X)^<ab> is infinite, and M a set of primes with Dirichlet density one. Using results from p-adic transcendental number theory, we show that K, p and the projection M → Spec Z can be recovered from the topological quandle Q(X, M) or Q^<ab>(X, M).続きを見る

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登録日 2019.12.03
更新日 2024.12.02

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