Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects

Released on by Fabrizio Andreatta
preview-18

  • Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects Book Detail

  • Author : Fabrizio Andreatta
  • Release Date : 2005
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 114
  • ISBN 13 : 0821836099
  • File Size : 20,20 MB
DOWNLOAD BOOK

Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects by Fabrizio Andreatta PDF Summary

Book Description: We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$ theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we define operators $U$, $V$ and $\Theta_\chi$ and study the variation of the filtration under these operators. Our methods are geometric - comparing holomorphic Hilbert modular forms with rational functions on a moduli scheme with level-$p$ structure, whose poles are supported on the non-ordinary locus.In the $p$-adic theory we study congruences between Hilbert modular forms. This applies to the study of congruences between special values of zeta functions of totally real fields. It also allows us to define $p$-adic Hilbert modular forms 'a la Serre' as $p$-adic uniform limit of classical modular forms, and compare them with $p$-adic modular forms 'a la Katz' that are regular functions on a certain formal moduli scheme. We show that the two notions agree for cusp forms and for a suitable class of weights containing all the classical ones. We extend the operators $V$ and $\Theta_\chi$ to the $p$-adic setting.

Disclaimer: www.yourbookbest.com does not own Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

P-adic Aspects Of Modular Forms

P-adic Aspects Of Modular Forms

File Size : 63,63 MB
Total View : 4397 Views
DOWNLOAD

The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first lo

Hilbert Modular Forms and Iwasawa Theory

Hilbert Modular Forms and Iwasawa Theory

File Size : 37,37 MB
Total View : 2595 Views
DOWNLOAD

The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly importa