Effective lifting of 2-cocycles for Galois cohomology

Thomas Preu

Open Mathematics (2013)

  • Volume: 11, Issue: 12, page 2138-2149
  • ISSN: 2391-5455

Abstract

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We give explicit formulas for reducing the problem of determining whether a given 2-cocycle is a coboundary and if so finding a lifting 1-cochain to a system of norm equations.

How to cite

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Thomas Preu. "Effective lifting of 2-cocycles for Galois cohomology." Open Mathematics 11.12 (2013): 2138-2149. <http://eudml.org/doc/269172>.

@article{ThomasPreu2013,
abstract = {We give explicit formulas for reducing the problem of determining whether a given 2-cocycle is a coboundary and if so finding a lifting 1-cochain to a system of norm equations.},
author = {Thomas Preu},
journal = {Open Mathematics},
keywords = {Galois cohomology; Local invariants; local invariants},
language = {eng},
number = {12},
pages = {2138-2149},
title = {Effective lifting of 2-cocycles for Galois cohomology},
url = {http://eudml.org/doc/269172},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Thomas Preu
TI - Effective lifting of 2-cocycles for Galois cohomology
JO - Open Mathematics
PY - 2013
VL - 11
IS - 12
SP - 2138
EP - 2149
AB - We give explicit formulas for reducing the problem of determining whether a given 2-cocycle is a coboundary and if so finding a lifting 1-cochain to a system of norm equations.
LA - eng
KW - Galois cohomology; Local invariants; local invariants
UR - http://eudml.org/doc/269172
ER -

References

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  1. [1] Bright M., Swinnerton-Dyer P., Computing the Brauer-Manin obstructions, Math. Proc. Cambridge Philos. Soc., 2004, 137(1), 1–16 http://dx.doi.org/10.1017/S0305004104007571 Zbl1057.14022
  2. [2] Brown K.S., Cohomology of Groups, Grad. Texts in Math., 87, Springer, New York-Berlin, 1982 http://dx.doi.org/10.1007/978-1-4684-9327-6 
  3. [3] Fesenko I.B., Vostokov S.V., Local Fields and Their Extensions, Transl. Math. Monogr., 121, American Mathematical Society, Providence, 2002 Zbl1156.11046
  4. [4] Fieker C., Über Relative Normgleichungen in Algebraischen Zahlkörpern, Dr. Rer. Nat. Dissertation, Technische Universität, Berlin, 1997 
  5. [5] Fieker C., Minimizing representations over number fields II: Computations in the Brauer group, J. Algebra, 2009, 322(3), 752–765 http://dx.doi.org/10.1016/j.jalgebra.2009.05.009 Zbl1177.20020
  6. [6] Hasse H., Beweis eines Satzes und Widerlegung einer Vermutung über das allgemeine Normenrestsymbol, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1931, 64–69 
  7. [7] Hilton P.J., Stammbach U., A Course in Homological Algebra, 2nd ed., Grad. Texts in Math., 4, Springer, New York, 1997 http://dx.doi.org/10.1007/978-1-4419-8566-8 Zbl0863.18001
  8. [8] Holt D.F., Cohomology and group extensions in Magma, In: Discovering Mathematics with Magma, Algorithms Comput. Math., 19, Springer, Berlin, 2006, 221–241 http://dx.doi.org/10.1007/978-3-540-37634-7_10 Zbl1146.20312
  9. [9] Kresch A., Tschinkel Yu., On the arithmetic of del Pezzo surfaces of degree 2, Proc. London Math. Soc., 2004, 89(3), 545–569 http://dx.doi.org/10.1112/S002461150401490X Zbl1075.14019
  10. [10] Kresch A., Tschinkel Yu., Effectivity of Brauer-Manin obstructions, Adv. Math., 2008, 218(1), 1–27 http://dx.doi.org/10.1016/j.aim.2007.11.017 Zbl1142.14013
  11. [11] Milne J.S., Étale Cohomology, Princeton Math. Ser., 33, Princeton University Press, Princeton, 1980 
  12. [12] Neukirch J., Algebraische Zahlentheorie, Springer, Berlin-Heidelberg, 2007 
  13. [13] Reid M., Chapters on algebraic surfaces, In: Complex Algebraic Geometry, Park City, 1993, IAS/Park City Math. Ser., 3, American Mathematical Society, Providence, 1997, 3–159 
  14. [14] Serre J.-P., Corps Locaux, Publications de l’Institut de Mathématique de l’Université de Nancago, VIII, Actualités Sci. Indust., 1296, Hermann, Paris, 1962 
  15. [15] Shatz S.S., Profinite Groups, Arithmetic, and Geometry, Ann. of Math. Stud., 67, Princeton University Press, Princeton, 1972 Zbl0236.12002
  16. [16] Yamamoto K., An explicit formula of the norm residue symbol in a local number field, Sci. Rep. Tokyo Woman’s Christian College, 1972, 24–28, 302–334 

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