Some remarks on the arithmetic Hodge index conjecture

Klaus Künnemann

Compositio Mathematica (1995)

  • Volume: 99, Issue: 2, page 109-128
  • ISSN: 0010-437X

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Künnemann, Klaus. "Some remarks on the arithmetic Hodge index conjecture." Compositio Mathematica 99.2 (1995): 109-128. <http://eudml.org/doc/90410>.

@article{Künnemann1995,
author = {Künnemann, Klaus},
journal = {Compositio Mathematica},
keywords = {standard conjectures of Grothendieck; arithmetic variety; Arakelov varieties; real Arakelov Chow groups},
language = {eng},
number = {2},
pages = {109-128},
publisher = {Kluwer Academic Publishers},
title = {Some remarks on the arithmetic Hodge index conjecture},
url = {http://eudml.org/doc/90410},
volume = {99},
year = {1995},
}

TY - JOUR
AU - Künnemann, Klaus
TI - Some remarks on the arithmetic Hodge index conjecture
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 99
IS - 2
SP - 109
EP - 128
LA - eng
KW - standard conjectures of Grothendieck; arithmetic variety; Arakelov varieties; real Arakelov Chow groups
UR - http://eudml.org/doc/90410
ER -

References

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  1. 1 Bachmat, E.: A Fourier transform construction for Arakelov Chow groups of arithmetic abelian schemes. Duke Math. J., Int. Math. Res. Notices, No. 7, (1993), 227-232. Zbl0851.14018MR1230299
  2. 2 Beilinson, A.A.: Higher regulators and values of L-functions. J. Soviet Math.30 (1985), 2036-2070. Zbl0588.14013
  3. 3 Bost, J-B., Gillet, H., Soulé C.: Heights of projective varieties and positive Green currents. Journal of the AMS7 (1994), 903-1027. Zbl0973.14013MR1260106
  4. 4 Deninger, C., Murre, J.: Motivic decomposition of abelian schemes and the Fourier transform. J. reine angew. Math.422 (1991), 201-219. Zbl0745.14003MR1133323
  5. 5 Fulton, W.: Intersection theory. Springer: Berlin-Heidelberg-New York1984. Zbl0541.14005MR732620
  6. 6 Gillet, H., Soulé C.: Arithmetic intersection theory. Publ. Math. I.H.E.S. 72 (1990), 94-174. Zbl0741.14012MR1087394
  7. 7 Gillet, H., Soulé C.: Arithmetic analogs of the standard conjectures. In: U. Jannsen, S. L. Kleiman, J-P. Serre: Proceedings of the conference on motives, Seattle 1991, Proceedings of Symposia in Pure Mathematics55I (1994), 129-140. Zbl0820.14007MR1265527
  8. 8 Gillet, H., Soulé C.: Characteristic classes for algebraic vector bundles with hermitian metrics I, II. Annals of Math.131 (1990), 163-238. Zbl0715.14006MR1038362
  9. 9 Künnemann, K.: A Lefschetz decomposition for Chow motives of abelian schemes. Invent. math.113 (1993), 85-102. Zbl0806.14001MR1223225
  10. 10 Künnemann, K.: Arakelov Chow groups of abelian schemes, arithmetic Fourier transform and analogues of the standard conjectures of Lefschetz type. Math. Ann.300 (1994), 365-392. Zbl0808.14020MR1304428
  11. 11 Moriwaki, A.: Hodge index theorem for arithmetic cycles of codimension one. Alg. geom. e-prints, March, 94. Zbl0873.14005
  12. 12 Wells, R.O., Jr.: Differential analysis on complex manifolds. Grad. texts in math.65, Springer: Berlin-Heidelberg-New York, 1980. Zbl0435.32004MR608414

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