First Beilinson’s conjecture in function fields arithmetic

Abstract: In the mid 80’s, Beilinson formulated deep conjectures relating special values of $L$-functions to pieces of $K$-theory, superseding at once the BSD conjecture and Deligne’s conjecture. Beilinson's conjectures are fully expressed in the framework of mixed motives, which remains hypothetical.

This talk will be devoted to portray the analogous picture in the function fields setting, using so-called Goss $L$-values instead of classical $L$-values, and mixed (uniformizable) Anderson $A$-motives instead of Grothendieck's mixed motives. After a recall of the classical conjectures, we shall discuss and define the analogue of motivic cohomology and regulators for function fields, and express the counterpart of Beilinson’s conjectures.

algebraic geometrynumber theory

Audience: researchers in the topic

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Rendez-vous on special values and periods

Series comments: The main objective of this conference is to gather together young researchers interested in special values of L-functions and periods. These objects are at the crossroads of many recent important developments in arithmetic geometry, such as Euler systems or the theory of motives. The different talks will portray the variety of viewpoints with which L-functions and periods are studied at present.

Registration is free and mandatory, to get access to the livestream and recording of the talks.

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