The norm of a canonical isomorphism of determinant line bundles

Thesis

We extend an involution formula given by a canonical isomorphism of determinant line bundles in Rössler’s [a] to the analytic case where the determinant of cohomology is endowed with the Quillen metric, in the case where the fixed point scheme is a Cartier divisor.

Additionally, we show the relation between Rössler’s main results in [a] and the Adams-Riemann-Roch theorem; and we extend the main result of Ducrot’s [b], which aims to extend Deligne’s pairing to the higher relative dimensional intersection bundle, to the analytic case.

[a] Damian Rössler, A local refinement of the Adams-Riemann-Roch theorem in degree 1, Arithmetic L-functions and differential geometric methods, Progr. Math., vol. 338, Birkhäuser/Springer, Cham, [2021], pp. 213–246.

[b] François Ducrot, Cube structures and intersection bundles, J. Pure Appl. Algebra, 195 (2005), no. 1, 33–73.

Authors: Gomezllata Marmolejo, E

• DOI: 10.5287/ora-6rqzr1jzj
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: cube structures; involution formula; quillen metric on the determinant of cohomology
• Subjects: Arithmetical algebraic geometry