Isotropy of quadratic forms over function fields of p -adic curves

R. Parimala; V. Suresh

Publications Mathématiques de l'IHÉS (1998)

  • Volume: 88, page 129-150
  • ISSN: 0073-8301

How to cite

top

Parimala, R., and Suresh, V.. "Isotropy of quadratic forms over function fields of $p$-adic curves." Publications Mathématiques de l'IHÉS 88 (1998): 129-150. <http://eudml.org/doc/104133>.

@article{Parimala1998,
author = {Parimala, R., Suresh, V.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {quadratic form; -invariant; -adic field; Galois cohomology; unramified cohomology; quadric fibration; zero-cycles; Cayley algebras},
language = {eng},
pages = {129-150},
publisher = {Institut des Hautes Études Scientifiques},
title = {Isotropy of quadratic forms over function fields of $p$-adic curves},
url = {http://eudml.org/doc/104133},
volume = {88},
year = {1998},
}

TY - JOUR
AU - Parimala, R.
AU - Suresh, V.
TI - Isotropy of quadratic forms over function fields of $p$-adic curves
JO - Publications Mathématiques de l'IHÉS
PY - 1998
PB - Institut des Hautes Études Scientifiques
VL - 88
SP - 129
EP - 150
LA - eng
KW - quadratic form; -invariant; -adic field; Galois cohomology; unramified cohomology; quadric fibration; zero-cycles; Cayley algebras
UR - http://eudml.org/doc/104133
ER -

References

top
  1. [A] A. A. ALBERT, Normal division algebras of degree four over an algebraic field, Trans. Amer. Math. Soc. 34 (1931), 363-372. Zbl0004.10002MR1501642JFM58.0144.01
  2. [Ar] J. K. ARASON, Cohomologische Invarianten quadratischer Formen, J. Algebra 36 (1975), 448-491. Zbl0314.12104MR52 #10592
  3. [AEJ] J. K. ARASON, R. ELMAN and B. JACOB, Fields of cohomological 2-dimension three, Math. Ann. 274 (1986), 649-657. Zbl0576.12025MR87m:12006
  4. [C] J.-L. COLLIOT-THÉLÈNE, Birational invariants, purity, and the Gresten conjecture, Proceedings of Symposia in Pure Math. 58 (1995), Part 1, 1-64. Zbl0834.14009MR96c:14016
  5. [CS] J.-L. COLLIOT-THÉLÈNE et J.-J. SANSUC, Fibres quadratiques et composantes connexes reelles, Math. Ann. 244 (1979), 105-134. Zbl0418.14016MR81c:14010
  6. [CSk] J.-L. COLLIOT-THÉLÈNE et A. N. SKOROBOGATOV, Groupe de Chow des zero-cycles sur les fibres en quadriques, K-Theory 7 (1993), 477-500. Zbl0837.14002MR95c:14012
  7. [Gre] M. J. GREENBERG, Lectures on forms in many variables, Benjamin, New York, Amsterdam 1969. Zbl0185.08304MR39 #2698
  8. [G] M. GROS, 0-cycles de degré zéro sur les surface fibrées en coniques, J. reine Angew. Math. 373 (1987), 166-184. Zbl0593.14005MR88h:14007
  9. [Gr] A. GROTHENDIECK, Le groupe de Brauer III, Dix exposés sur la cohomologie des schémas, Amsterdam, North-Holland, Amsterdam (1968), 88-188. Zbl0198.25901
  10. [HV] D. W. HOFFMANN and J. VAN GEEL, Zeroes and norm groups of quadratic forms over function fields in one variable over a local non-dyadic field, J. Ramanujan Math. Soc. 13 (1998), 85-110. Zbl0922.11032MR2000c:11058
  11. [K] K. KATO, A Hasse principle for two-dimensional global fields, J. reine Angew. Math. 366 (1986), 142-181. Zbl0576.12012MR88b:11036
  12. [L] S. LICHTENBAUM, Duality theorems for curves over p-adic fields, Invent. Math. 7 (1969), 120-136. Zbl0186.26402MR39 #4158
  13. [M1] A. S. MERKURJEV, On the norm residue symbol of degree 2, Dokl. Akad. Nauk. SSSR 261 (1981), 542-547. Zbl0496.16020MR83h:12015
  14. [M2] A. S. MERKURJEV, Division algebras over p-adic curves. Report on Saltman's work, lectures at UCL, june 1997, handwritten notes by J.-P. Tignol. Zbl0902.16021
  15. [O] M. OJANGUREN, Quadratic forms over regular rings, J. Indian Math. Soc. 44 (1980), 109-116. Zbl0621.10017MR85h:11017
  16. [P] R. PARIMALA, Witt groups of affine three folds, Duke Math. J. 57 (1989), 947-954. Zbl0674.14029MR90a:14006
  17. [PS] R. PARIMALA and V. SURESH, Zero-cycles on quadric fibrations, finiteness theorems and the cycle map, Invent. Math. 122 (1995), 83-117. Zbl0865.14002MR96i:14005
  18. [S] D. J. SALTMAN, Division Algebras over p-adic curves, J. Ramanujan Math. Soc. 12 (1997), 25-47. Zbl0902.16021MR98d:16032
  19. [S1] D. J. SALTMAN, Correction to Division algebras over p-adic curves, J. Ramanujan Math. Soc. 13 (1998), 125-130. Zbl0920.16008MR99k:16036
  20. [Sc] W. SCHARLAU, Quadratic and Hermitian Forms, Grundlehren der Math. Wiss., Vol. 270, Berlin, Heidelberg, New York 1985. Zbl0584.10010MR86k:11022
  21. [Se] J. P. SERRE, Cohomologie Galoisienne : Progrès et Problèmes, Séminaire Bourbaki, 783 (1993-94). Zbl0837.12003
  22. [T] J. TATE, Relations between K2 and Galois cohomology, Invent. Math. 36 (1976), 257-274. Zbl0359.12011MR55 #2847

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.