Siegel modular variety of degree two and level four by Ronnie Lee

Cover of: Siegel modular variety of degree two and level four | Ronnie Lee

Published by American Mathematical Society in Providence, R.I .

Written in English

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Subjects:

  • Siegel domains.,
  • Modular groups.,
  • Homology theory.,
  • Hodge theory.

Edition Notes

Book details

Other titlesCohomology of the Siegel modular group of degree two and level four.
StatementRonnie Lee, Steven H. Weintraub. Cohomology of the Siegel modular group of degree two and level four / J. William Hoffman, Steven H. Weintraub.
SeriesMemoirs of the American Mathematical Society,, no. 631
ContributionsWeintraub, Steven H., Hoffman, Jerome William, 1952-, Hoffman, Jerome William, 1952-
Classifications
LC ClassificationsQA3 .A57 no. 631, QA331 .A57 no. 631
The Physical Object
Paginationix, 75 p. ;
Number of Pages75
ID Numbers
Open LibraryOL343755M
ISBN 100821806203
LC Control Number98002692

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Cohomology of the Siegel Modular Group of Degree Two and Level Four, by J. William Hoffman and Steven H. Weintraub The authors compute the cohomology of the principal congruence subgroup \(\Gamma_2(4) \subset S{_p4}(\mathbb Z)\) consisting of matrices \(\gamma \equiv \mathbf 1\) mod 4.

Lee R., Weintraub S.H. () The siegel modular variety of degree two and level four: A report. In: Barth WP., Lange H. (eds) Arithmetic of Complex Manifolds. Lecture Cited by: 3. The Siegel modular variety of degree two and level four (by Ronnie Lee and Steven H.

Weintraub) Cohomology of the Siegel modular group of degree two and level four (by J. William Hoffman and Steven H. Weintraub). The Siegel modular variety of degree two and level four (by Ronnie Lee and Steven H.

Weintraub) 0. Introduction 1. Algebraic background 2. Geometric background 3. Taking stock 4. Type III A 5.

Type II A 6. Type II B 7. Type IV C 8. Let A2(n) denote the quotient of the Siegel upper half space of degree two by Γ2(n), the principal congruence subgroup of level n in Sp(4, Z). A2(n) is the moduli space of principally polarized abelian varieties of dimension two with a level n structure, and has a.

The siegel modular variety of degree two and level four: A report.- Some effective estimates for elliptic curves.- A pencil of K3- surfaces related to Apery's.

Let A2(n) = Γ2(n)\G fraktur sign2 be the quotient of Siegel's space of degree 2 by the principal congruence subgroup of level n in Sp(4, ℤ). This is the moduli space of principally polarized Author: Jae-Hyun Yang. Ronnie Lee and Steven H. Weintraub, The Siegel modular variety of degree two and level four: a report, Arithmetic of complex manifolds (Erlangen, ) Lecture Notes in Math., vol.Springer, Berlin,pp.

89– The Siegel Modular Variety Of Degree Two And Level Three. By J. William, J. William Hoffman and Steven H. Weintraub. Abstract. Let A2 (n) denote the quotient of the Siegel upper half space of degree two by \Gamma 2 (n), the principal congruence subgroup of level n in Sp(4; Z).

A2 (n) is the moduli space of principally polarized abelian. I want to emphasize that Siegel modular forms play an important role in the theory of the arithmetic and the geometry of the Siegel modular variety Ag. The aim of this paper is to discuss a theory of the Siegel modular variety in the aspects of arithmetic and geometry.

Unfortunately two important subjects, which are the theory of. For the theory of the cohomology of the Siegel modular variety (in particular of degree two) we refer to [20], [58, 59], [87], [88] and [, ].

Labesse and Schwermer [85] used two kinds of. Products of Siegel modular forms. Level 1, small degree. For degree 1, the level 1 Siegel modular forms are the same as level 1 modular forms.

The ring of such forms is a polynomial ring C[E 4,E 6] in the (degree 1) Eisenstein series E 4 and E 6. Cohomology of the Siegel modular group of degree two and level four J. William Ho man and Steven H. Weintraub Abstract We compute the cohomology of the subgroup of the integral sym-plectic group of degree 2 consisting of matrices 1 mod 4.

This is done by computing the cohomology of the moduli space of principally. The aim of this paper is to discuss a theory of the Siegel modular variety in the aspects of arithmetic and geometry.

Unfortunately two important subjects, which are the theory of harmonic analysis on the Siegel modular variety, and the Galois representations associated to Siegel modular forms are not covered in this article. Given a Hilbert modular form of weight (2,2n+ 2) e prove the existence of a non-zero Siegel modular form of degree 2 and weight n + 2forthe ramodular congruence subgroup.

Our main theorem completely characterizes the resulting Siegel odular form, including the Cited by: Part of the Lecture Notes in Mathematics book series (LNM, volume ) Log in to check access. Buy eBook. USD The siegel modular variety of degree two and level four: A report.

Ronnie Lee, Steven H. Weintraub. On the cohomology of siegel modular threefolds. Rainer Weissauer. Pages Back Matter. the Siegel modular group of degree two and level four / J. Representation Theory of Finite Groups Algebra and Arithmetic, Steven H.

Weintraub,Mathematics, pages. Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. This book presents an introduction to the representation theory of finite. on siegel modular varieties of level 3 TOMOYOSHI IBUKIYAMA Departement of Mathematics, College of General Education, Kyushu University, RopponmatsuFukuoka,JapanCited by: The Siegel Modular Variety of Degree Two and Level Four, IssueRonnie Lee, Steven H.

Weintraub, Jerome William Hoffman, Jan 1,Mathematics, 75 pages. Enthält: The Siegel modular variety of degree two and level four / Ronnie Lee, Steven H.

Weintraub. Cohomology of. In this thesis we consider various aspects of the theory of Siegel modular forms on the congruence subgroup 0(N). The basic motivation is that the theta function for higher Eisenstein series of degree two, squarefree level and trivial nebentypus, the key novelty 4 Fourier coe cients of level N Siegel{Eisenstein series 64 File Size: KB.

William H. Hoffman: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books. 5, Books 4. Williams Obstetrics, 25th Edition. McGraw-Hill Education / Medical The Siegel Modular Variety of Degree Two and Level Four. Amer Mathematical Society.

Ronnie Lee, Steven H. Weintraub. a consequence of our main theorem, there exists a non-zero Siegel modular form F of degree 2 and weight 3 for the paramodular group of level N = 2 2 3 2 5 4 such that Λ(s, F) Λ(s, ρ).

The paper is organized as follows. We denote the space of cusp forms on $\Sp(4,\Z)$ of weight $(j,k)$, i.e. corresponding to $\Sym^j$ tensor $\det^k$, by $S_{j,k}$.

For chosen weight $(j,k)$ with $k. The Siegel Modular Variety of Degree Two and Level Four/Cohomology of the Siegel Modular Group of Degree Two and Level Four. Book The Siegel Modular Variety of Degree Two and Level Four, by Ronnie Lee and Steven H. Weintraub Let $\mathbf M_n$ denote the quotient of the degree two Siegel space by the principal congruence subgroup of level.

It was the aim of the Erlangen meeting in May to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms.

In recent years such problems, which are. On an algebra of Siegel modular forms associated with the theta group γ_2(1,2) Kogiso, Takeyoshi and Tsushima, Koji, Tsukuba Journal of Mathematics, ; Iwahori-spherical representations of GSp(4) and Siegel modular forms of degree 2 with square-free level SCHMIDT, Ralf, Journal of the Mathematical Society of Japan, of scalar-valued Siegel modular forms and a degree 8 map between two given Siegel modular threefolds.

The results of this section are based on my paper [39]. We will prove that the degree 8 map P 3. P [x 0,x 1x 2,x 3] 7![x20,x2 x2 2,x 2 3],(1) is a map between two Siegel modular varieties. This is the part that will give the right.

Discover Book Depository's huge selection of Steven H Weintraub books online. Free delivery worldwide on over 20 million titles. The Siegel Modular Variety of Degree Two and Level Four/Cohomology of the Siegel Modular Group of Degree Two and Level Four.

Ronnie Lee. 01 Jun Paperback. unavailable. Notify me. Algebra. Four dimensional symplectic geometry over the field with three elements and a moduli space of abelian surfaces, Note Mat. 20 (/01), no.

1, ; MR e Hoffman, J. William and Weintraub, Steven H., The Siegel modular variety of degree two and level three, Trans. Amer. Math. Soc. (), no. 8, ; MR b Steven H.

Weintraub: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books. 5, Books 4. Differential Forms: A Complement to Vector Calculus.

Academic Press The Siegel Modular Variety of Degree Two and Level Four. Amer Mathematical Society. Ronnie Lee, Steven H. Weintraub. Based on this theory, we will extend Igusa’s result [6] on Siegel modular forms over C, i.e., show that the ring of Siegel full modular forms of degree 2 over any Z[1/6]-algebra is generated by the two normalized Eisenstein series of weight 4, 6 and by the three normalized cusp forms of wei 12, Cited by: 5.

PART 2: SIEGEL MODULAR FORMS AARON POLLACK 1. Siegel modular forms We now begin to discuss Siegel modular forms. Siegel modular forms are special automorphic forms for the symplectic group Sp 2n.

Recall that Sp 2n= fg2GL n: g 0 1n 1n 0 gt= 0 1n 1n g: Equivalently, and more canonically if you prefer, Sp 2n is the group preserving a non-degenerate. Siegel modular cusp forms of any given weight.

So far, these dimensions are only known for scalar-valued Siegel modular forms by work of Tsuyumine, and our results agree with this.

For g = 2, the dimensions of most spaces of Siegel cusp forms were known earlier, so the dimension predictions are a new feature in genus Size: KB. Siegel modular variety of degree two and level fourcohomology of the Siegel modular group of degree two and level four.

By Ronnie Lee, Steven H Weintraub and J William Hoffman. Topics: Mathematical Physics and Mathematics. The Siegel modular variety A g (n), which parametrize principally polarized abelian varieties of dimension g with a level n-structure, arises as the quotient of the Siegel upper half-space by the action of the principal congruence subgroup of level n of a symplectic group.

The Siegel Modular Variety of Degree Two and Level Four (Memoirs of the American Mathematical Society) by Ronnie Lee, Steven H. Weintraub, Jerome William Hoffman, American Mathematical Society Hardcover, 75 Pages, Published by Amer Mathematical Society ISBNISBN: Steven H.

Weintraub has 15 books on Goodreads with ratings. Steven H. Weintraub’s most popular book is Differential Forms: A Complement to Vector Cal.

We describe some examples of projective Calabi-Yau manifolds which arise as desingularizations of Siegel threefolds. There is a certain explicit product of six theta constants which defines a cusp form of weight three for a certain subgroup of index two of the Hecke group Γ 2, 0 [2].This form defines an invariant differential form for this group and for any subgroup of by: 3.

$G_2$ Forms. We refer to and for the definition of a Siegel modular cusp form of degree $3$ of type $G_2$. We list the cases where the dimension of $S_{j,k,l}$ with. Siegel Varieties and p-Adic Siegel Modular Forms then be posed in a similar way. It would then require a similar study of the (rigid) geometry of Shimura varieties of parahoric type for the corresponding groups.

Part of this paper has been written during visits at NCTS (Taiwan) and CRM (Montreal). Moduli spaces of Riemann surfaces of genus two with level structures: On the transformation law for theta constants: Representation theory of finite groups: algebra and arithmetic: Rochlin invariants, theta functions, and the holonomy of some determinant line bundles: The Siegel modular variety of degree two and level four.of the theory, like the Siegel modular group and its action on the Siegel upper half-space, reduction theory, examples of Siegel modular forms, Hecke operators and L-functions.

Secondly, following up, I would like to discuss two rather recent research topics, namely the ”Ikeda lifting” and sign changes of Hecke eigenvalues in genus Size: KB.types of infinite-dimensional representations containing non-trivial vec-tors fixed under the local Siegel congruence subgroup, while in the GL(2) case we had only 2 (see table (1)).

• There is currently no generally accepted notion of newforms for Siegel modular forms of degree 2. The last two problems are of course related.

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