Details
| Original language | English |
|---|---|
| Pages (from-to) | 241-270 |
| Number of pages | 30 |
| Journal | Algebra and Number Theory |
| Volume | 15 |
| Issue number | 1 |
| Publication status | Published - 1 Mar 2021 |
Abstract
We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have very large degree. Our results also hold in characteristic two, where they solve the rationality problem for hypersurfaces under a logarithmic degree bound, thereby extending a previous result of the author from characteristic different from two to arbitrary characteristic.
Keywords
- Algebraic cycles, Hypersurfaces, Rationality, Unirationality, Unramified cohomology
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Algebra and Number Theory, Vol. 15, No. 1, 01.03.2021, p. 241-270.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Torsion orders of Fano hypersurfaces
AU - Schreieder, Stefan
PY - 2021/3/1
Y1 - 2021/3/1
N2 - We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have very large degree. Our results also hold in characteristic two, where they solve the rationality problem for hypersurfaces under a logarithmic degree bound, thereby extending a previous result of the author from characteristic different from two to arbitrary characteristic.
AB - We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have very large degree. Our results also hold in characteristic two, where they solve the rationality problem for hypersurfaces under a logarithmic degree bound, thereby extending a previous result of the author from characteristic different from two to arbitrary characteristic.
KW - Algebraic cycles
KW - Hypersurfaces
KW - Rationality
KW - Unirationality
KW - Unramified cohomology
UR - http://www.scopus.com/inward/record.url?scp=85103029401&partnerID=8YFLogxK
U2 - 10.2140/ant.2021.15.241
DO - 10.2140/ant.2021.15.241
M3 - Article
VL - 15
SP - 241
EP - 270
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 1
ER -