摘要翻译：
设R为实闭域，且a=R[x_1,...,x_n]。设sper A表示A的实谱。在sper A中有两类点：有限点（所有x_1，…，x_n都以R中的某个常数为界）和无穷远点。本文研究了sper A无穷远点集的结构及其相关的赋值。设T是{1，…，n}的子集。对于{1,...,n}中的j,若j不在T中,设Y_j=X_j,若j在T中,设Y_j=1/X_j,设B_t=R[y_1,...,Y_n]。我们将sper A表示为U_T形式集合的不交并，并构造了每个集合U_T与sper B_t的有限点空间的子空间的同胚。对于U_T中无穷远处的每个点d，我们用与d相关的估值v_d来描述其像d*在sper B_T中的相关估值v_{d*}。其中，我们证明了赋值环v_{d*}是由v_d构成的（换句话说，赋值环R_d是R_{d*}在适当素理想上的局部化）。
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英文标题：
《On points at infinity of real spectra of polynomial rings》
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作者：
Fran\c{c}ois Lucas (LAREMA), Daniel Schaub (LAREMA), Mark Spivakovsky
  (LEP)
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Let R be a real closed field and A=R[x_1,...,x_n]. Let sper A denote the real spectrum of A. There are two kinds of points in sper A : finite points (those for which all of |x_1|,...,|x_n| are bounded above by some constant in R) and points at infinity. In this paper we study the structure of the set of points at infinity of sper A and their associated valuations. Let T be a subset of {1,...,n}. For j in {1,...,n}, let y_j=x_j if j is not in T and y_j=1/x_j if j is in T. Let B_T=R[y_1,...,y_n]. We express sper A as a disjoint union of sets of the form U_T and construct a homeomorphism of each of the sets U_T with a subspace of the space of finite points of sper B_T. For each point d at infinity in U_T, we describe the associated valuation v_{d*} of its image d* in sper B_T in terms of the valuation v_d associated to d. Among other things we show that the valuation v_{d*} is composed with v_d (in other words, the valuation ring R_d is a localization of R_{d*} at a suitable prime ideal).
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PDF链接：
https://arxiv.org/pdf/0707.2327