Hilbert Modular Forms mod p and p Adic Aspects is popular PDF and ePub book, written by Fabrizio Andreatta in 2005, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Hilbert Modular Forms mod p and p Adic Aspects can be Read Online from any device for your convenience.
Hilbert Modular Forms mod p and p Adic Aspects Book PDF Summary
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.
Detail Book of Hilbert Modular Forms mod p and p Adic Aspects PDF
- Author : Fabrizio Andreatta
- Release : 20 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821836095
- Genre : Mathematics
- Total Page : 114 pages
- Language : English
- PDF File Size : 19,5 Mb
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