Let be a proper smooth variety over a field of characteristic and an effective divisor on with multiplicity. We introduce a generalized Albanese variety Alb of of modulus , as higher dimensional analogue of the generalized Jacobian with modulus of Rosenlicht-Serre. Our construction is algebraic. For we give a Hodge theoretic description.
Soient une variété propre et lisse sur un corps de caractéristique et un diviseur effectif avec multiplicité sur . Nous introduisons une variété d’Albanese généralisée Alb de , de module , comme analogue en dimension supérieure de la jacobienne généralisée avec module de Rosenlicht-Serre. Notre construction est algébrique. Si , nous donnons une description en termes de théorie de Hodge.
Keywords: generalized Albanese variety, modulus of a rational map, generalized mixed Hodge structure
Mot clés : variété d’Albanese généralisée, module d’une fonction, structure de Hodge mixte généralisée
Kato, Kazuya 1; Russell, Henrik 2
@article{AIF_2012__62_2_783_0, author = {Kato, Kazuya and Russell, Henrik}, title = {Albanese varieties with modulus and {Hodge} theory}, journal = {Annales de l'Institut Fourier}, pages = {783--806}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {2}, year = {2012}, doi = {10.5802/aif.2694}, mrnumber = {2985516}, zbl = {1261.14023}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2694/} }
TY - JOUR AU - Kato, Kazuya AU - Russell, Henrik TI - Albanese varieties with modulus and Hodge theory JO - Annales de l'Institut Fourier PY - 2012 SP - 783 EP - 806 VL - 62 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2694/ DO - 10.5802/aif.2694 LA - en ID - AIF_2012__62_2_783_0 ER -
%0 Journal Article %A Kato, Kazuya %A Russell, Henrik %T Albanese varieties with modulus and Hodge theory %J Annales de l'Institut Fourier %D 2012 %P 783-806 %V 62 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2694/ %R 10.5802/aif.2694 %G en %F AIF_2012__62_2_783_0
Kato, Kazuya; Russell, Henrik. Albanese varieties with modulus and Hodge theory. Annales de l'Institut Fourier, Volume 62 (2012) no. 2, pp. 783-806. doi : 10.5802/aif.2694. https://aif.centre-mersenne.org/articles/10.5802/aif.2694/
[1] Formal Hodge theory, Math. Res. Lett., Volume 14 (2007) no. 3, pp. 385-394 | MR
[2] Sharp de Rham realization, Adv. Math., Volume 222 (2009) no. 4, pp. 1308-1338 | DOI | MR
[3] Albanese and Picard 1-motives, Mém. Soc. Math. Fr. (N.S.) (2001) no. 87, pp. vi+104 | Numdam | MR | Zbl
[4] Enriched Hodge structures, Algebra, arithmetic and geometry, Part I, II (Mumbai, 2000) (Tata Inst. Fund. Res. Stud. Math.), Volume 16, Tata Inst. Fund. Res., Bombay, 2002, pp. 171-184 | MR
[5] Théorie de Hodge. II et III, Inst. Hautes Études Sci. Publ. Math. (1971 et 1974) no. 40 et 44, p. 5-78 et 5–77 | DOI | Numdam | Zbl
[6] The universal regular quotient of the Chow group of points on projective varieties, Invent. Math., Volume 135 (1999) no. 3, pp. 595-664 | DOI | MR | Zbl
[7] On the de Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. (1966) no. 29, pp. 95-103 | DOI | Numdam | MR | Zbl
[8] Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture Notes in Mathematics, No. 20, Springer-Verlag, Berlin, 1966 | MR
[9] Transformation de Fourier généralisée, 1996 (Preprint arXiv:alg-geom/9603004)
[10] Generalized Albanese and its dual, J. Math. Kyoto Univ., Volume 48 (2008) no. 4, pp. 907-949 | MR | Zbl
[11] Albanese varieties with modulus over a perfect field, 2010 (Preprint arXiv:0902.2533v2) | Zbl
Cited by Sources: