The tropical Nullstellensatz for congruences

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• 作者：Aaron Bertram¹ ; ^{bertram@math.utah.edu} ; Robert Easton ; ^{rweaston@calpoly.edu}
• 关键词：14T05 ; 16Y60
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：21 February 2017
• 年：2017
• 卷：308
• 期：Complete
• 页码：36-82
• 全文大小：766 K
• 卷排序：308

文摘

We develop the foundations of a theory of algebraic geometry for semirings, concentrating mainly on the semiring of tropical polynomials. Replacing ideals with the more general notion of congruences, we establish a relationship between congruences on the semiring of tropical polynomials and subsets of tropical space. We ultimately establish analogues of the weak and strong forms of Hilbert's Nullstellensatz.