On Frobenius and Fibers of Arithmetic Jet Spaces

Borger, James; Saha, Arnab

doi:10.48550/arxiv.1703.07010

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The Lateral Frobenius and Characters Of N N1

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2019

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“…Here we would also like to remark that the lateral Frobenius can also be constructed in the mixed-characteristic setting of p-jet spaces of arbitrary schemes [BoSa1], but it is much more involved.…”

Section: The Lateral Frobenius and Characters Of N Nmentioning

confidence: 99%

Differential characters of Drinfeld modules and de Rham cohomology

Borger

Saha

2019

Alg. Number Th.

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We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differential characters of elliptic curves in differential algebra, both of which have had notable Diophantine applications. We determine the structure of the group of differential characters. This shows the existence of a family of interesting differential modular functions on the moduli of Drinfeld modules. It also leads to a canonical F -crystal equipped with a map to the de Rham cohomology of the Drinfeld module. This F -crystal is of a differential-algebraic nature, and the relation to the classical cohomological realizations is presently not clear.

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Section: The Lateral Frobenius and Characters Of N Nmentioning

confidence: 99%