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

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

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

R. T. Kundnani,

V. Marimuthu,

K. Alam,

Sh. Kant

2026-06-11

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. The main result proves that boundary vanishing of the top Hodge Chern class is preserved by lci-type derived pullbacks. We further isolate a non-tautological criterion under which a concrete system of lci derived boundary tests detects the tautological boundary kernel and identifies it with the ideal generated by the top Hodge class.

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.

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