On the Grothendieck ring of varieties in positive characteristic
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910208268173312 |
|---|---|
| author | Joshi, Kirti |
| author_facet | Joshi, Kirti |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_02614 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the Grothendieck ring of varieties in positive characteristic Joshi, Kirti Algebraic Geometry Number Theory 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. |
| title | On the Grothendieck ring of varieties in positive characteristic |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/1811.02614 |