LECTURE 8. THE GROTHENDIECK RING OF VARIETIES AND KAPRANOV’S MOTIVIC ZETA FUNCTION In this lecture we give an introduction to the Grothendieck ring of algebraic varieties, and discuss Kapranov’s lifting of the Hasse-Weil zeta function to this Grothendieck ring
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چکیده
In this lecture we give an introduction to the Grothendieck ring of algebraic varieties, and discuss Kapranov’s lifting of the Hasse-Weil zeta function to this Grothendieck ring. One interesting feature is that this makes sense over an arbitrary field. We will prove the rationality of Kapranov’s zeta function for curves by a variant of the argument used in Lecture 4 for the Hasse-Weil zeta function. We will end by discussing the results of Larsen and Lunts on Kapranov zeta functions of algebraic surfaces.
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