The Arithmetic Theory of Local Constants for abelian Varieties

Marco Adamo Seveso

Rendiconti del Seminario Matematico della Università di Padova (2012)

  • Volume: 127, page 17-40
  • ISSN: 0041-8994

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Seveso, Marco Adamo. "The Arithmetic Theory of Local Constants for abelian Varieties." Rendiconti del Seminario Matematico della Università di Padova 127 (2012): 17-40. <http://eudml.org/doc/275105>.

@article{Seveso2012,
author = {Seveso, Marco Adamo},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Selmer group of an abelian variety; -perity conjecture for Selmer groups},
language = {eng},
pages = {17-40},
publisher = {Seminario Matematico of the University of Padua},
title = {The Arithmetic Theory of Local Constants for abelian Varieties},
url = {http://eudml.org/doc/275105},
volume = {127},
year = {2012},
}

TY - JOUR
AU - Seveso, Marco Adamo
TI - The Arithmetic Theory of Local Constants for abelian Varieties
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2012
PB - Seminario Matematico of the University of Padua
VL - 127
SP - 17
EP - 40
LA - eng
KW - Selmer group of an abelian variety; -perity conjecture for Selmer groups
UR - http://eudml.org/doc/275105
ER -

References

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  1. [1] F. Andreatta - E. Z. Goren, Geometry of Hilbert modular varieties over totally ramified primes, Internat. Math. Res. Notices, 33 (2003), pp. 1785–1835. Zbl1045.14012MR1987504
  2. [2] S. Bloch - K. Kato, L-functions and Tamagawa numbers of motives, in: The Grothendieck Festschrift, Vol. I, Prog. in Math. 86, Birkhauser, Boston (1990), P. Cartier, et al., eds., pp. 333–400. Zbl0768.14001MR1086888
  3. [3] P. Deligne - G. Pappas, Singularités des espaces de modules de Hilbert, en les caractérisque divisant le discriminant, Compos. Math., 90, No. 1 (1994), pp. 59–79. Zbl0826.14027MR1266495
  4. [4] M. Flach, A generalisation of the Cassels-Tate pairing, J. Reine Angew. Math., 412 (1990), pp. 113–127. Zbl0711.14001MR1079004
  5. [5] G. van der Geer, Abelian varieties. Manuscript available at http://staff.science.uva.nl/~bmoonen/boek/BookAV.html. Zbl0698.14047
  6. [6] B. H. Gross - J. Parson, On the local divisibility of Heegner points. Lang Memorial Volume. Zbl1276.11091
  7. [7] B. Mazur - K. Rubin, Finding large Selmer rank via an arithmetic theory of local constants, Ann. of Math. (2), 166, No. 2 (2007), pp. 579–612. Zbl1219.11084MR2373150
  8. [8] B. Mazur - K. Rubin - A. Silverberg, Twisting commutative algebraic groups, J. Algebra, 314, No. 1 (2007), pp. 419–438. Zbl1128.14034MR2331769
  9. [9] J. S. Milne, Etale cohomology, Princeton University Press (1980). Zbl0433.14012MR559531
  10. [10] D. Mumford, Abelian varieties, Oxford University Press (1970). Zbl0583.14015MR282985
  11. [11] Jan Nekovár, Selmer complexes, Astérisque, 310 (2006). Zbl1211.11120MR2333680
  12. [12] M. Rapoport, Compactifications de l'Espace de Modules de Hilbert-Blumenthal, Compos. Math., 36 (1978), pp. 255–335. Zbl0386.14006MR515050
  13. [13] M. A. Seveso, Stark-Heegner points and Selmer groups of abelian varieties, PhD Thesis, University of Milan, Federigo Enriques Department of Mathematics. 
  14. [14] M. A. Seveso, Congruences and rationality of Stark-Heegner points, to appear in the Journal of Number Theory, doi: 10.1016/j.jnt.2011.10.001. Zbl1308.11063MR2875348
  15. [15] G. Tamme, Introduction to étale cohomology, Springer-Verlag (1994). Zbl0815.14012MR1317816

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