Vanishing of Boundary Chern Classes under Derived Base Change on Toroidal Compactifications

Rahul Thakurdas Kundnani,Vinoth  Marimuthu,Khursheed  Alam,Shri  Kant

ПРЕПРИНТ

Эта статья является препринтом и не была отрецензирована.
О результатах, изложенных в препринтах, не следует сообщать в СМИ как о проверенной информации.

Vanishing of Boundary Chern Classes under Derived Base Change on Toroidal Compactifications

R. T. Kundnani,

V. Marimuthu,

K. Alam,

Sh. Kant

2026-08-15

https://doi.org/10.24108/preprints-3115505

We study the behavior of the top Chern class of the Hodge bundle on toroidal compactifications of moduli spaces of abelian varieties under derived base change. We distinguish throughout between ordinary operational restriction and refined/virtual Gysin pullback. The main result proves that the refined boundary cycle associated with the top Hodge Chern class is preserved under quasi-smooth derived base change. When the ordinary operational boundary restriction vanishes, the corresponding refined boundary cycle vanishes and hence so do all of its quasi-smooth derived boundary pullbacks. We further describe how quasi-smooth derived boundary tests factor through the refined boundary operator and record the resulting conditional consequence for tautological boundary kernels.

Ссылка для цитирования:

Kundnani R. T., Marimuthu V., Alam K., Kant Sh. 2026. Vanishing of Boundary Chern Classes under Derived Base Change on Toroidal Compactifications. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115505

Список литературы

1. W. Fulton, Intersection Theory, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, vol. 2, Springer-Verlag, Berlin, 1998.

2. G. Faltings and C.-L. Chai, Degeneration of Abelian Varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 22, Springer-Verlag, Berlin, 1990.

3. D. Mumford, “Hirzebruch's proportionality theorem in the non-compact case,” Inventiones Mathematicae, vol. 42, 1977, pp. 239–272.

4. A. Kresch, “Cycle groups for Artin stacks,” Inventiones Mathematicae, vol. 138, no. 3, 1999, pp. 495–536.

5. B. Toën and G. Vezzosi, Homotopical Algebraic Geometry II: Geometric Stacks and Applications, Memoirs of the American Mathematical Society, vol. 193, no. 902, 2008.

6. C. Manolache, “Virtual pull-backs,” Journal of Algebraic Geometry, vol. 21, no. 2, 2012, pp. 201–245.

7. A. A. Khan, “Virtual fundamental classes of derived stacks I,” arXiv:1909.01332v1 [math.AG], 2019.

8. J. Lurie, Higher Algebra, version of September 18, 2017, available from the author's webpage.

9. D. Gaitsgory and N. Rozenblyum, A Study in Derived Algebraic Geometry. Vol. II: Deformations, Lie Theory and Formal Geometry, Mathematical Surveys and Monographs, vol. 221, American Mathematical Society, Providence, RI, 2017.

10. H. Gillet and C. Soulé, “Arithmetic intersection theory,” Publications Mathématiques de l'IHÉS, vol. 72, 1990, pp. 93–174.

11. J. I. Burgos Gil, J. Kramer, and U. Kühn, “Arithmetic characteristic classes of automorphic vector bundles,” Documenta Mathematica, vol. 10, 2005, pp. 619–716.

ПРЕПРИНТ

ИНФОРМАЦИЯ

Использование куки-файлов