Complex multiplication cycles and Kudla-Rapoport divisors
نویسندگان
چکیده
منابع مشابه
Complex Multiplication Cycles and Kudla-rapoport Divisors Ii
This paper is about the arithmetic of Kudla-Rapoport divisors on Shimura varieties of type GU(n− 1, 1). In the first part of the paper we construct a toroidal compactification of N. Krämer’s integral model of the Shimura variety. This extends work of K.-W. Lan, who constructed a compactification at unramified primes. In the second, and main, part of the paper we use ideas of Kudla to construct ...
متن کاملHeights of Kudla–Rapoport divisors and derivatives of L-functions
We study special cycles on integral models of Shimura varieties associated with unitary similitude groups of signature (n−1, 1). We construct an arithmetic theta lift from harmonic Maass forms of weight 2 − n to the arithmetic Chow group of the integral model of a unitary Shimura variety, by associating to a harmonic Maass form f a linear combination of Kudla– Rapoport divisors, equipped with t...
متن کاملNOTICE : Stephen S . Kudla , Michael Rapoport , and Tonghai Yang
is published by Princeton University Press and copyrighted, © 2006, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users ar...
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This paper concerns two families of divisors, which we call the ‘orthogonal’ and ‘unitary’ special cycles, defined on integral models of Shimura curves. The orthogonal family was studied extensively by Kudla-Rapoport-Yang, who showed that they are closely related to the Fourier coefficients of modular forms of weight 3/2, while the unitary divisors are analogues of cycles appearing in more rece...
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We review the history of elliptic curves and show that it is possible to form a group law using the points on an elliptic curve over some field L. We review various methods for computing the order of this group when L is finite, including the complex multiplication method. We then define and examine the properties of elliptic pairs, lists, and cycles, which are related to the notions of amicabl...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2012
ISSN: 0003-486X
DOI: 10.4007/annals.2012.176.2.9