Document Type
Article
Publication Date
2004
Publication Title
Compositio Mathematica
Abstract
We introduce a new approach to the study of a system of algebraic equations in (C) whose Newton polytopes have sufficiently general relative positions. Our method is based on the theory of Parshin’s residues and tame symbols on toroidal varieties. It provides a uniform algebraic explanation of the recent result of Khovanskii on the product of the roots of such systems and the Gel’fond–Khovanskii result on the sum of the values of a Laurent polynomial over the roots of such systems, and extends them to the case of an algebraically closed field of arbitrary characteristic.
Repository Citation
Soprunov, Ivan, "Residues and Tame Symbols on Toroidal Varieties" (2004). Mathematics and Statistics Faculty Publications. 274.
https://engagedscholarship.csuohio.edu/scimath_facpub/274
DOI
10.1112/S0010437X0400079X
Version
Postprint
Publisher's Statement
The final publication is available at Springer via http://dx.doi.org/10.1112/S0010437X0400079X
Volume
140
Issue
6
