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Rigid Meromorphic Cocycles and P-Adic Families of Modular Forms

Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems January 23, 2023 - January 27, 2023

January 27, 2023 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Alice Pozzi (Imperial College, London)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
  • p-adic geometry

  • explicit class field theory

  • algebraic cycles

  • number theory

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Rigid Meromorphic Cocycles And P-Adic Families Of Modular Forms

Abstract

Rigid meromorphic cocycles are classes in the first cohomology of SL_2(Z[1/p]) acting on the non-zero rigid meromorphic functions on the Drinfeld p-adic upper half plane. Their values at real quadratic points are conjectured to be analogues of singular moduli for real quadratic fields. In this talk, I will discuss the relation between real quadratic singular moduli and derivatives of p-adic families of modular forms. These results can be fit into an emerging p-adic Kudla program. 

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Rigid Meromorphic Cocycles And P-Adic Families Of Modular Forms

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