Last edited by Malale
Tuesday, May 5, 2020 | History

4 edition of Moduli of Abelian varieties found in the catalog.

# Moduli of Abelian varieties

Written in English

Subjects:
• Abelian varieties.,
• Moduli theory.

• Edition Notes

Includes bibliographical references and indexes.

Classifications The Physical Object Statement Allan Adler, S. Ramanan. Series Lecture notes in mathematics -- 1644 Contributions Ramanan, S. LC Classifications QA3, QA564 Pagination vi,196p. ; Number of Pages 196 Open Library OL22343183M ISBN 10 3540620230

The material about abelian varieties (the third chapter of the article) is quite comparable to the beginning of Mumford's book, pointed out by Emerton. Finally, I think that the study of abelian varieties can hardly be dissociated from the study of Riemann surfaces, because historically abelian varieties appeared as Jacobians of Riemann surfaces. Now back in print, the revised edition of this popular study gives a systematic account of the basic results about abelian varieties. Mumford describes the analytic methods and results applicable when the ground field k is the complex field C and discusses the scheme-theoretic methods and results used to deal with inseparable isogenies when the ground field k has characteristic p.

TITLE={Moduli of abelian varieties in mixed and in positive characteristic}, NOTE={[to appear in the {\it Handbook of Moduli} (G. Farkas and I. Morrison, eds.), International Press of Boston, Someverville, MA, and Higher Education Press, Beijing, ]},Cited by: In Section 2 we discuss each of these three points of view of the moduli of principally polarized abelian varieties (and moduli of abelian varieties with higher degree polarization). Then in sections 3 and 4 we discuss how each of these three approaches leads to different compactiﬁcations (toroidal, Alexeev, and Ag respectively).

Lecture 2: Abelian varieties The subject of abelian varieties is vast. In these notes we will hit some highlights of the theory, stressing examples and intuition rather than proofs (due to lack of time, among other reasons). We will note analogies with the more concrete case of elliptic curves (as in [Si]), asFile Size: KB. Ben Moonen A dimension formula for Ekedahl-Oort strata. Ann. de l'Institut Fourier 54 (), Ben Moonen Group schemes with additional structures and Weyl group cosets. In: Moduli of abelian varieties (Texel Island, ), , Progress in Math. , Birkhäuser, Bas Edixhoven, Ben Moonen and Frans Oort.

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Abelian varieties and their moduli are a central topic of increasing importance in todays mathematics. Applications range from algebraic geometry and number theory to mathematical physics.

The present collection of 17 refereed articles originates from the third "Texel Conference" held in Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool.

For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry.

It begins with a generalization of parts of Mumford's theory of the equations defining abelian varieties and moduli spaces. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

: Moduli of Curves and Abelian Varieties: The Dutch Intercity Seminar on Moduli (Aspects of Mathematics) (): Carel Faber, Eduard Looijenga: Books. Abelian varieties and their moduli are a central topic of increasing importance in todays mathematics.

Applications range from algebraic geometry and number theory to mathematical physics. The present collection of 17 refereed articles originates from the third "Texel Conference" held in Leading experts discuss and study the structure of the moduli spaces of abelian varieties and. new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles.

Topics include a stratification of a moduli space of abelian varieties in positive characteristic, and the calculation of the classes of the strata, tautological classes for moduli of abelian varieties as well as.

In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed precisely, Siegel modular varieties are the moduli spaces of principally polarized abelian varieties of a fixed dimension.

They are named after Carl Ludwig Siegel, a 20th-century German mathematician who specialized in number theory. Get this from a library. Moduli of Abelian varieties. [C Faber; Gerard van der Geer; Frans Oort;] -- "Abelian varieties and their moduli are a central topic of increasing importance in today's mathematics.

Applications range from algebraic geometry and number theory to mathematical physics." "The. Moduli spaces for abelian varieties over C. Kevin Buzzard Ap Last modi ed August 1 Introduction. These are some notes I wrote in order to teach myself the classical analytic theory of moduli spaces for abelian varieties.

They may well contain mistakes, and they might have a \lop-sided" feel because they emphasize only the partsFile Size: KB. Also, abelian varieties play a significant role in the geometric approach to modern algebraic number theory.

In this book, Kempf has focused on the analytic aspects of the geometry of abelian varieties, rather than taking the alternative algebraic or arithmetic points of view.

His purpose is to provide an introduction to complex analytic geometry. This is a continuation of the previous paper and book, applying that theory in particular to moduli of abelian varieties. Hirzebruch's Proportionality Theorem in the non-compact case, Invent.

Math., pp. Scanned reprint and DASH reprint. I'm looking for an accessible reference for the fact that the moduli stack of principally polarized abelian varieties is in fact an algebraic stack.

Faltings/Chai sketch two possible proofs in their book on degenerations of abelian varieties but I don't think I will be able to get the details from this source. book, applying that theory in particular to moduli of abelian varieties. Hirzebruch's Proportionality Theorem in the non-compact case, Invent.

Math., pp. Scanned reprint and DASH reprint Tata Lectures on Theta (with C. Musili, Madhav Nori, File Size: 29KB. This contains the proof that the moduli space polarized abelian varieties (of sufficiently large degree) with level structure is representable. It's also dense, especially considering it's contained within a huge book a lot of the material of which you might not want to learn.

Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

The book will appeal to pure mathematicians, especially algebraic geometers and number theorists, but will also be relevant for researchers in mathematical physics.

MODULI OF ABELIAN VARIETIES JESSE LEO KASS LECTURE 1 (November 6, - Jesse Kass) In this lecture we recall the complex analytic construction of the Torelli map and then explain how to construct this map using algebraic geometry. We begin by xing g 1and working over the eld of complex numbers k= C.

De ne H g equal to the Siegel upper half-plane. Moduli of CM abelian varieties. In the main it follows Mum-ford’s book [16] except that most results are stated relative to an arbitrary base field, some additional results are proved, and Author: Frans Oort.

The topic of this book is the theory of degenerations of abelian varieties and its application to the construction of compactifications of moduli spaces of abelian varieties. These compactifications have applications to diophantine problems and, of course, are also interesting in their own right.

By P Norman and F OORT, Published on 01/01/ Recommended Citation. Norman, P and OORT, F, "MODULI OF ABELIAN-VARIETIES" ().Cited by:. This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa.

This provides a different approach to compactifying these spaces than the more classical approach using toroical.The geometric description of Abelian varieties in terms of uniformizing spaces and lattices plays a central role in compactifying moduli spaces of Abelian varieties.

To compactify, the idea is to enlarge to a stack in such a way that the valuative criterion of properness holds. Moduli of abelian varieties in mixed and in positive characteristic Frans Oort. Local models of Shimura varieties, I: Geometry and combinatorics Georgios Pappas, Michael Rapoport and Brian Smithling.

Generalized theta linear series on moduli spaces of vector bundles on curves Mihnea Popa. Computer aided unirationality proofs of moduli spaces.