Titlebook: Arithmetic L-Functions and Differential Geometric Methods; Regulators IV, May 2 Pierre Charollois,Gerard Freixas i Montplet,Vincen Conferen

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Automatic Property Declaration,We prove that the Adams–Riemann–Roch theorem in degree one (i.e., at the level of the Picard group) can be lifted to an isomorphism of line bundles, compatibly with base change.

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Toric Regulators,In the mid-19th century, Dirichlet (for quadratic fields) and then Dedekind defined a regulator map relating the units in the ring of integers of an algebraic number field of finite degree over Q with r. real embeddings and 2r.complex embeddings to a lattice of codimension one in a Euclidean space of dimension r. + r..

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,A Local Refinement of the Adams–Riemann–Roch Theorem in Degree One,We prove that the Adams–Riemann–Roch theorem in degree one (i.e., at the level of the Picard group) can be lifted to an isomorphism of line bundles, compatibly with base change.

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Persistence and the Data Portal, equipped with the structure of a higher display which is a relative version of Fontaine’s strongly divisible lattices. Frobenius-divisibility is induced by the Nygaard filtration on the relative de Rham–Witt complex. For a nilpotent PD-thickening . we also consider the associated relative display a

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Business Object Implementation,’s curvature theorem. Then we introduce Bismut–K?hler analytic torsion form for an orbifold K?hler fibration. Finally we calculate the behaviour of the Quillen metric by orbifold submersions as an extension of Berthomieu– Bismut’s result.

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https://doi.org/10.1007/978-1-4302-4861-3d by Ray–Singer in order to give a definition of Reidemeister torsion for a closed Riemannian manifold. This torsion was conjectured to be equal to the analytic torsion defined by purely analytic means, which was proven shortly afterwards by Cheeger and Müller. We will give a short account of this t