Extensions with restricted ramification and duality for arithmetic schemes

Alexander Schmidt

Compositio Mathematica (1996)

  • Volume: 100, Issue: 2, page 233-245
  • ISSN: 0010-437X

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Schmidt, Alexander. "Extensions with restricted ramification and duality for arithmetic schemes." Compositio Mathematica 100.2 (1996): 233-245. <http://eudml.org/doc/90428>.

@article{Schmidt1996,
author = {Schmidt, Alexander},
journal = {Compositio Mathematica},
keywords = {restricted ramification; arithmetic surfaces; étale homotopy group; arithmetic scheme; sheaf cohomology; étale cohomology; duality theorem; étale fundamental group},
language = {eng},
number = {2},
pages = {233-245},
publisher = {Kluwer Academic Publishers},
title = {Extensions with restricted ramification and duality for arithmetic schemes},
url = {http://eudml.org/doc/90428},
volume = {100},
year = {1996},
}

TY - JOUR
AU - Schmidt, Alexander
TI - Extensions with restricted ramification and duality for arithmetic schemes
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 100
IS - 2
SP - 233
EP - 245
LA - eng
KW - restricted ramification; arithmetic surfaces; étale homotopy group; arithmetic scheme; sheaf cohomology; étale cohomology; duality theorem; étale fundamental group
UR - http://eudml.org/doc/90428
ER -

References

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  1. 1 Artin, M., Grothendieck, A. and Verdier, J.L.: Theorie des Topos et Cohomologie Etale des Schemas(SGA4)LNM269, 270, 305. 
  2. 2 Artin M., Mazur, B.: Etale HomotopyLNM100Springer1969. Zbl0182.26001MR245577
  3. 3 Friedlander, E.M.: Etale homotopy of simplicial schemesAnn. of Math. Studies104Princeton Univ. Press1982. Zbl0538.55001MR676809
  4. 4 Haberland, K.: Galois cohomology of algebraic number fieldsDt. Verlag der Wissenschaften, Berlin1978. Zbl0418.12004MR519872
  5. 5 Milne, J.S.: Etale CohomologyPrinceton University Press1980. Zbl0433.14012MR559531
  6. 6 Milne, J.S.: Arithmetic Duality Theorems Persp. in Math. 1 Academic PressBoston1986. Zbl0613.14019MR881804
  7. 7 Neukirch, J.: Einbettungsprobleme mit lokaler Vorgabe und freie Produkte lokaler GaloisgruppenJ. f. reine u. ang. Math. 259 (1973) 1-47. Zbl0263.12006MR347773
  8. 8 Schmidt, A., Wingberg, K.: On the fundamental group of a smooth arithmetic surfaceMath. Nachr. 159 (1992) 19-36. Zbl0793.14008MR1237099
  9. 9 Serre, J.P.: Cohomologie GaloisienneLecture Notes in Math. 5Springer1964. Zbl0136.02801
  10. 10 Tate, J.: Letter to Serre in [9]. Zbl0284.12004
  11. 11 Verdier, J.L.: Dualité dans la cohomologie des groupes profinies in [9]. 
  12. 12 Washington, L.C.: Class Numbers and Zp-Extensions Math.Ann.214 (1975) 177-193. Zbl0302.12007MR364182
  13. 13 Wingberg, K.: On Galois groups ofp-closed algebraic number fields with restricted ramificationJ. reine u. ang. Math.400 (1989) 185-202 Zbl0715.11065MR1013730

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