Residues and tame symbols on toroidal varieties

Details Residues and tame symbols on toroidal varieties Residues and tame symbols on toroidal varieties

2002-03-12

arxiv.org/abs/math/0203114v3

Compositio Math. 140 (2004) no. 6, 1593--1613

Mathematics

Algebraic Geometry

26 pages, minor changes, title changed, new introduction, references added

Scientific paper

We introduce a new approach to the study of a system of algebraic equations in the algebraic torus 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.

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