主理想域上多项式环理想的合性

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI:10.1145/3373207.3404046

H. Charalambous, K. Karagiannis, Sotiris Karanikolopoulos, A. Kontogeorgis

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引用次数: 0

摘要

我们研究了多项式环R[w1，…]上的梯度模的协同的计算方面。，当基R是一个离散赋值环时。特别地，我们利用它们在R上的合子的扭转提供了一个公式，该公式描述了将基改为R的剩余场或分数场时Betti数的行为。

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Syzygies of ideals of polynomial rings over principal ideal domains

We study computational aspects of syzygies of graded modules over polynomial rings R[w1, ..., wg] when the base R is a discrete valuation ring. In particular, we use the torsion of their syzygies over R to provide a formula which describes the behavior of the Betti numbers when changing the base to the residue field or the fraction field of R. Our work is motivated by the deformation theory of curves.

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Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation

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