Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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
References:
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$$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
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 199, Issue 3, Pages 302–305
DOI: https://doi.org/10.1007/s10958-014-1857-4
Bibliographic databases:
Document Type: Article
UDC: 512.743
Language: English
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
Citation in format AMSBIB
\Bibitem{Kar13}
\by N.~A.~Karpenko
\paper Incompressibility of generic torsors of norm tori
\inbook Problems in the theory of representations of algebras and groups. Part~25
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 414
\pages 106--112
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5668}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 199
\issue 3
\pages 302--305
\crossref{https://doi.org/10.1007/s10958-014-1857-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902302806}
Linking options:
  • https://www.mathnet.ru/eng/znsl5668
  • https://www.mathnet.ru/eng/znsl/v414/p106
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:138
    Full-text PDF :41
    References:53
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024