# 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

**Speaker(s):**Alice Pozzi (Imperial College, London)

**Location:**SLMath: Eisenbud 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

#### Rigid Meromorphic Cocycles And P-Adic Families Of Modular Forms

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.

#### Rigid Meromorphic Cocycles And P-Adic Families Of Modular Forms

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