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1994 | OriginalPaper | Buchkapitel

Projective Lines Over One-Dimensional Semilocal Domains and Spectra of Birational Extensions

verfasst von : William Heinzer, David Lantz, Sylvia Wiegand

Erschienen in: Algebraic Geometry and its Applications

Verlag: Springer New York

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In [7], Nashier asked if the condition on a one-dimensional local domain R that each maximal ideal of the Laurent polynomial ring R[y, y-1] contracts to a maximal ideal in R[y] or in R[y-1] implies that R is Henselian. Motivated by this question, we consider the structure of the projective line Proj(R[s, t]) over a one-dimensional semilocal domain R (the projective line regarded as a topological space, or equivalently as a partially ordered set). In particular, we give an affirmative answer to Nashier’s question. (Nashier has also independently answered his question [9].) Nashier has also studied implications on the prime spectrum of the Henselian property in [8] as well as in the papers cited above.

Metadaten
Titel
Projective Lines Over One-Dimensional Semilocal Domains and Spectra of Birational Extensions
verfasst von
William Heinzer
David Lantz
Sylvia Wiegand
Copyright-Jahr
1994
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4612-2628-4_19