STNB2022 (35è any)

Artin formalism and Euler systems


Óscar Rivero Salgado


A useful source of analogies in the study of Euler systems is based on considering situations where one cusp form degenerates to an Eisenstein series. In this talk, I will discuss two different approaches to this question. The first one relies on the study of congruences between Euler systems when one cusp form is congruent to an Eisenstein series, which has been partially studied in a joint work with Victor Rotger. The second one considers Coleman families passing through a critical p-stabilization of an Eisenstein series and allows us to recover, for instance, Beilinson--Flach classes beginning with diagonal cycles. This last part is a joint work with David Loeffler, that I will discuss in different scenarios, emphasizing possible applications.


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