|
Zapiski Nauchnykh Seminarov POMI, 2013, Volume 414, Pages 106–112
(Mi znsl5668)
|
|
|
|
Incompressibility of generic torsors of norm tori
N. A. Karpenko Université Pierre et Marie Curie, Institut de Mathématiques de Jussieu, Paris, France
Abstract:
Let $p$ be a prime integer, $F$ be a field of characteristic not $p$, $T$ the norm torus of a degree $p^n$ extension field of $F$, and $E$ a $T$-torsor over $F$ such that the degree of each closed point on $E$ is divisible by $p^n$ (a generic $T$-torsor has this property). We prove that $E$ is $p$-incompressible. Moreover, all smooth compactifications of $E$ (including those given by toric varieties) are $p$-incompressible. The main requisites of the proof are: (1) A. Merkurjev's degree formula (requiring the characteristic assumption), generalizing M. Rost's degree formula, and (2) combinatorial construction of a smooth projective fan invariant under an action of a finite group on the ambient lattice due to J.-L. Colliot-Thélène–D. Harari–A. N. Skorobogatov, produced by refinement of J.-L. Brylinski's method with a help of an idea of K. Künnemann.
Key words and phrases:
algebraic tori, toric varieties, incompressibility, Chow groups and Steenrod operations.
Received: 28.08.2012
Citation:
N. A. Karpenko, “Incompressibility of generic torsors of norm tori”, Problems in the theory of representations of algebras and groups. Part 25, Zap. Nauchn. Sem. POMI, 414, POMI, St. Petersburg, 2013, 106–112; J. Math. Sci. (N. Y.), 199:3 (2014), 302–305
Linking options:
https://www.mathnet.ru/eng/znsl5668 https://www.mathnet.ru/eng/znsl/v414/p106
|
Statistics & downloads: |
Abstract page: | 138 | Full-text PDF : | 41 | References: | 53 |
|