Réunion d'hiver SMC 2024
Vancouver/Richmond, 29 novembre - 2 decembre 2024
Arithmetic Aspects of Galois Representations
Org: Debanjana Kundu (UTRGV) et Antonio Lei (University of Ottawa)
Org: Debanjana Kundu (UTRGV) et Antonio Lei (University of Ottawa)
- RAUL ALONSO, UC Santa Barbara
- ADITHYA CHAKRAVARTHY, Toronto
- PAVEL COUPEK, MSU
- KIM TUAN DO, UCLA
- PAYMAN ESKANDARI, Winnipeg
- CHI-YUN HSU, Santa Clara
- HEEJONG LEE, Purdue
- SIMONE MALETTO, UBC
- TAM NGUYEN, UBC
- PEIKAI QI, Michigan State University
An analogue of Greenberg pseudo-null conjecture for CM fields [PDF]
- ADITHYA CHAKRAVARTHY, Toronto
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We will give an analogue of Greenberg's pseudo-null conjecture for CM fields. Let $K$ be a CM field and $K^+$ be the unique totally real subfield of $K$. Assume that primes above $p$ in $K^+$ all splits in $K$. Let $\mathfrak{P}_1,\mathfrak{P}_2,\cdots,\mathfrak{P}_s, \tilde{\mathfrak{P}}_1,\tilde{\mathfrak{P}}_2,\cdots,\tilde{\mathfrak{P}}_s$ be prime ideas in $K$ above $p$, where $\tilde{\mathfrak{P}}_i$ is the complex conjugation of $\mathfrak{P}_i$. We show that there is unique $\mathbb{Z}_p$-extension of $K$ unramified outside $\mathfrak{P}_1,\mathfrak{P}_2,\cdots,\mathfrak{P}_s$. We also show that such $\mathbb{Z}_p$-extension for CM field has similar properties as cyclotomic $\mathbb{Z}_p$-extension of a totally real field. We also give some criteria for Iwasawa invariant $\mu=\lambda=0$. The work is joint with Matt Stokes.
- SUJATHA RAMDORAI, UBC
- DANIEL VALLIERES, California State University Chico
- ILA VARMA, University of Toronto
- VINAYAK VATSAL, UBC
- DANIEL VALLIERES, California State University Chico