Conservativity and finite dimensional conjecture for Motives

点击翻译按钮获取中文摘要

Algebraic varieties are the spaces defined as the zero sets of polynomials. Closed sub algebraic varieties are parametrized also by algebraic varieties, called Chow varieties. The main result of this research is that the power series taking these Chow varieties(of important varieties such as Toric varieties) as coefficients become rational functions, under the relation called A^1 homotopy. A^1 homotopy naturally arises in non-commutative motives, related to physical mathematics, and our result implies that Chow varieties must be deeply related to physical mathematics.