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Yuan Yang
Yuan Yang
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I did a little search work on this problem, and it seems that I found the following article answered it perfectly. \

The Lefschetz trace formula for algebraic stacks \

The result is that: If $\mathcal{X}$ is an algebraic stack, the we will have a same Lefschetz trace formula for $\mathcal{X}$, but it would not always be a finite sum. But if it is Deligne-Mumford, then it is known that it is a finite sum, so we do have the rationality of its zeta-function.

I did a little search work on this problem, and it seems that the following article answered it perfectly. \

The Lefschetz trace formula for algebraic stacks \

The result is that: If $\mathcal{X}$ is an algebraic stack, the we will have a same Lefschetz trace formula for $\mathcal{X}$, but it would not always be a finite sum. But if it is Deligne-Mumford, then it is known that it is a finite sum, so we do have the rationality of its zeta-function.

I did a little search work on this problem, and it seems that I found the following article. \

The Lefschetz trace formula for algebraic stacks \

The result is that: If $\mathcal{X}$ is an algebraic stack, the we will have a same Lefschetz trace formula for $\mathcal{X}$, but it would not always be a finite sum. But if it is Deligne-Mumford, then it is known that it is a finite sum, so we do have the rationality of its zeta-function.

Source Link
Yuan Yang
Yuan Yang
  • 547
  • 3
  • 10

I did a little search work on this problem, and it seems that the following article answered it perfectly. \

The Lefschetz trace formula for algebraic stacks \

The result is that: If $\mathcal{X}$ is an algebraic stack, the we will have a same Lefschetz trace formula for $\mathcal{X}$, but it would not always be a finite sum. But if it is Deligne-Mumford, then it is known that it is a finite sum, so we do have the rationality of its zeta-function.