On the Grothendieck ring of varieties in positive characteristic

2018/11/06 by Joshi, Kirti · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1811.02614

Abstract

This paper proves two theorems (1) Let k be an algebraically closed field of characteristic p>0. I prove (Theorem 2.1.1) that if, p > 13 or p = 11, then the isomorphism class of any supersingular elliptic curve is a zero divisor in the ring of smooth, complete k-varieties and Bittner relations. In particular, this ring contains zero divisors. The proof proceeds via establishing (in Theorem 2.2.1) that the Albanese variety functor is a motivic measure. (2) I prove (Theorem 3.1) that the etale fundamental group of a smooth, proper variety over any alg. clsoed field k (in any characteristic) also provides a motivic measure on this ring. In particular, the etale fundamental group is a motivic measure on the Grothendieck ring of varieties over complex numbers.

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