Comments on: q-analogues and homogeneous spaces http://concretenonsense.wordpress.com/2009/04/28/q-analogues-and-homogeneous-spaces/ A group blog about mathematics Tue, 01 Dec 2009 16:53:01 +0000 http://wordpress.com/ hourly 1 By: Steven Sam http://concretenonsense.wordpress.com/2009/04/28/q-analogues-and-homogeneous-spaces/#comment-202 Steven Sam Sun, 10 May 2009 02:06:03 +0000 http://concretenonsense.wordpress.com/?p=452#comment-202 I don't think we have to assume anything other than what I said. I have it written up here: http://math.mit.edu/~ssam/writings/calderochapoton.pdf (Lemma 2.2) I'm not very familiar with the Weil conjectures, but I think the technique used to prove this theorem is utilized. I don’t think we have to assume anything other than what I said. I have it written up here:
http://math.mit.edu/~ssam/writings/calderochapoton.pdf (Lemma 2.2)

I’m not very familiar with the Weil conjectures, but I think the technique used to prove this theorem is utilized.

]]> By: Zygmund http://concretenonsense.wordpress.com/2009/04/28/q-analogues-and-homogeneous-spaces/#comment-201 Zygmund Sun, 10 May 2009 00:46:41 +0000 http://concretenonsense.wordpress.com/?p=452#comment-201 "Theorem. Let X be a variety defined over Z and assume for some prime p, and all r>0, that the function is obtained by plugging in into some polynomial P(t). Then P(t) has integral coefficients, and P(1) is the Euler characteristic of (computed using cohomology with compact support)." Under what conditions is this true? It seems like an interesting theorem. (Is this related to the Weil conjectures? I remeber something like this was true for elliptic curves.) “Theorem. Let X be a variety defined over Z and assume for some prime p, and all r>0, that the function is obtained by plugging in into some polynomial P(t). Then P(t) has integral coefficients, and P(1) is the Euler characteristic of (computed using cohomology with compact support).”

Under what conditions is this true? It seems like an interesting theorem. (Is this related to the Weil conjectures? I remeber something like this was true for elliptic curves.)

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