| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
When X is a finite set, the formal sum of its symmetric products is rational, and the degree of its denominator is the number of the elements of X. When Y is an algebraic variety over a finite field, the rationality of the formal sum of the number of elements of its symmetric products is the celebrated Weil Conjecture, which promoted the advance of algebraic geometry in 20th century. The aim of this research is study the rationality of the formal sum of symmetric products (which is called the motivic zeta) in many categories.
We studied the rationality of the Motivic Chow Series, which is a generalization of the motivic zeta in the category of motives of algebraic varieties, and found that the rationality depends on the varieties and the equivalence relations, which implies the subtlety of this business. We also defined the generating function (expedited to be promoted to a version of motivic zeta), conjectured that it is always rational, and proved the rationality in some cases.
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