Supersingular curves of genus two and class numbers
Tomoyoshi Ibukiyama; Toshiyuki Katsura; Frans Oort
Compositio Mathematica (1986)
- Volume: 57, Issue: 2, page 127-152
- ISSN: 0010-437X
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topIbukiyama, Tomoyoshi, Katsura, Toshiyuki, and Oort, Frans. "Supersingular curves of genus two and class numbers." Compositio Mathematica 57.2 (1986): 127-152. <http://eudml.org/doc/89752>.
@article{Ibukiyama1986,
author = {Ibukiyama, Tomoyoshi, Katsura, Toshiyuki, Oort, Frans},
journal = {Compositio Mathematica},
keywords = {polarization; characteristic p; Jacobian variety; supersingular elliptic curves; prescribed automorphism group; curves of genus two; Hasse-Witt- matrix; class numbers of quaternionic algebras},
language = {eng},
number = {2},
pages = {127-152},
publisher = {Martinus Nijhoff Publishers},
title = {Supersingular curves of genus two and class numbers},
url = {http://eudml.org/doc/89752},
volume = {57},
year = {1986},
}
TY - JOUR
AU - Ibukiyama, Tomoyoshi
AU - Katsura, Toshiyuki
AU - Oort, Frans
TI - Supersingular curves of genus two and class numbers
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 57
IS - 2
SP - 127
EP - 152
LA - eng
KW - polarization; characteristic p; Jacobian variety; supersingular elliptic curves; prescribed automorphism group; curves of genus two; Hasse-Witt- matrix; class numbers of quaternionic algebras
UR - http://eudml.org/doc/89752
ER -
References
top- [1] M. Deuring: Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Univ. Hamburg14 (1941) 197-272. Zbl0025.02003MR5125JFM67.0107.01
- [2] M. Eichler: Über die Idealklassenzahl total definiter Quaternionenalgebren. Math. Z.43 (1938) 102-109. Zbl0017.15003MR1545717JFM63.0093.02
- [3] M. Eichler: Über die Idealklassenzahl hyperkomplexer Systeme. Math. Z.43 (1938) 481-494. Zbl0018.20201MR1545733JFM64.0085.01
- [4] M. Eichler: Zur Zahlentheorie der Quaternionen-Algebren. J. Reine Angew. Math.195 (1955) 127-151. Zbl0068.03303MR80767
- [5] K. Hashimoto: Class numbers of positive definite ternary quaternion hermitian forms. Proceed. Japan Acad.59 Ser. A (1983) 490-493. Zbl0539.10020MR732595
- [6] K. Hashimoto and T. Ibukiyama: On class numbers of positive definite binary quaternion hermitian forms (I). J. Fac. Sci. Univ. Tokyo Sect IA, 27 (1980) 549-601, (II) ibid. 28 (1981) 695-699,(III) ibid. to appear. Zbl0493.10030MR603952
- [7] T. Hayashida: A class number associated with the product of an elliptic curve with itself. J. Math. Soc. Japan20 (1968) 26-43. Zbl0186.26501MR233804
- [8] J. Igusa: Class number of a definite quaternion with prime discriminant. Proc. Nat. Acad. Sci. U.S.A.44 (1958) 312-314. Zbl0081.03601MR98728
- [9] J. Igusa: Arithmetic variety of moduli for genus two. Ann. of Math.72 (1960) 612-649. Zbl0122.39002MR114819
- [10] T. Katsura and F. Oort: Families of supersingular abelian surfaces. In preparation. Zbl0636.14017
- [11] N. Koblitz: P-adic variation of the zeta-function over families defined over finite fields. Compositio Math.31 (1975) 119-218. Zbl0332.14008MR414557
- [12] S. Lang: Abelian Varieties. New York: Interscience-Wiley (1959). Zbl0098.13201MR106225
- [13] Yu. I. Manin: The theory of commutative formal groups over fields of finite characteristic. Russian Math. Surveys18 (1963) 1-83. Zbl0128.15603MR157972
- [14] D. Mumford: Abelian Varieties. Oxford University Press (1970). Zbl0223.14022MR282985
- [15] P. Norman and F. Oort: Moduli of abelian varieties. Ann. of Math.112 (1980) 413-439. Zbl0483.14010MR595202
- [16] N.O. Nygaard: Slopes of powers of frobenius on crystalline cohomology. Ann. Sci. Ecole Norm. Sup.14 (1981) 369-401. Zbl0519.14012MR654203
- [17] F. Oort: Subvarieties of moduli spaces. Invent. Math.24 (1974) 95-119. Zbl0259.14011MR424813
- [18] F. Oort: Which abelian surfaces are products of elliptic curves? Math. Ann.214 (1975) 35-47. Zbl0283.14007MR364264
- [19] G. Shimura: Arithmetic of alternating forms and quaternion hermitian forms. J. Math. Soc. Japan15 (1963) 33-65. Zbl0121.28102MR146172
- [20] T. Shioda: Some results on unirationality of algebraic surfaces. Math. Ann.230 (1977) 153-168. Zbl0343.14021MR572983
- [21] T. Shioda: Supersingular K3 surfaces. Lecture Notes in Math.732. Berlin- Heidelberg-New York: Springer (1979) 564-591. Zbl0414.14019MR555718
- [22] W.C. Waterhouse: Abelian varieties over finite fields. Ann. Sci. Ecole Norm. Sup.2 (1962) 521-560. Zbl0188.53001MR265369
- [23] N. Yui: On the Jacobian varieties of hyperelliptic curves over fields of characteristic p > 2. Journ. of Alg.52 (1978) 378-410. Zbl0404.14008MR491717
Citations in EuDML Documents
top- Tomoyoshi Ibukiyama, Toshiyuki Katsura, On the field of definition of superspecial polarized abelian varieties and type numbers
- Yuri G. Zarhin, Non-supersingular hyperelliptic jacobians
- Toshiyuki Katsura, Frans Oort, Families of supersingular abelian surfaces
- Stephen S. Kudla, Michael Rapoport, Cycles on Siegel threefolds and derivatives of Eisenstein series
- Eyal Z. Goren, Kristin E. Lauter, Class Invariants for Quartic CM Fields
- Everett W. Howe, Enric Nart, Christophe Ritzenthaler, Jacobians in isogeny classes of abelian surfaces over finite fields
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