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Article Dans Une Revue Acta Mathematica Vietnamica Année : 2020

Recent developments in the theory of Anderson modules

Résumé

Let K be a global function field over a finite field of characteristic p and let A be the ring of elements of K which are regular outside a fixed place of K. This report presents recent developments in the arithmetic of special L-values of Anderson A-modules. Provided that p does not divide the class number of K, we prove an "analytic class number formula" for Anderson A-modules with the help of a recent work of Debry. For tensor powers of the Carlitz module, we explain how to derive several log-algebraicity results from the class number formula for these Anderson modules.
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Dates et versions

hal-01914776 , version 1 (07-11-2018)

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Bruno Anglès, Tuan Ngo Dac, Floric Ribeiro Tavares. Recent developments in the theory of Anderson modules. Acta Mathematica Vietnamica, 2020, 45, pp.199-216. ⟨10.1007/s40306-019-00348-z⟩. ⟨hal-01914776⟩
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