By David Mumford, C. P. Ramanujam, Yuri Manin

Now again in print, the revised version of this well known examine offers a scientific account of the elemental effects approximately abelian types. Mumford describes the analytic equipment and effects acceptable whilst the floor box ok is the advanced box C and discusses the scheme-theoretic equipment and effects used to accommodate inseparable isogenies whilst the floor box ok has attribute p. the writer additionally offers a self-contained facts of the lifestyles of a twin abeilan kind, stories the constitution of the hoop of endormorphisms, and contains in appendices "The Theorem of Tate" and the "Mordell-Weil Thorem." this can be a longtime paintings by way of an eminent mathematician and the one publication in this topic.

Show description

Read Online or Download Abelian varieties PDF

Similar algebraic geometry books

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (3rd Edition) (Undergraduate Texts in Mathematics)

This e-book information the center and soul of contemporary commutative and algebraic geometry. It covers such issues because the Hilbert foundation Theorem, the Nullstellensatz, invariant conception, projective geometry, and size thought. as well as improving the textual content of the second one variation, with over two hundred pages reflecting adjustments to reinforce readability and correctness, this 3rd version of beliefs, kinds and Algorithms contains: a considerably up to date part on Maple; up-to-date info on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; and offers a shorter facts of the Extension Theorem.

Essays in Constructive Mathematics

Contents and therapy are clean and intensely diversified from the normal remedies provides a completely optimistic model of what it capability to do algebra The exposition isn't just transparent, it's pleasant, philosophical, and thoughtful even to the main naive or green reader

Arithmetic Algebraic Geometry: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Trento, Italy, June 24-July 2, 1991 (Lecture Notes in Mathematics)

This quantity comprises 3 lengthy lecture sequence by means of J. L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their subject matters are respectively the relationship among algebraic K-theory and the torsion algebraic cycles on an algebraic type, a brand new method of Iwasawa conception for Hasse-Weil L-function, and the purposes of arithemetic geometry to Diophantine approximation.

Extra resources for Abelian varieties

Example text

N. Statement: Then there is a unique immersion X ∈ C3 (B, Rn+2 ) with an unique ONF N = (N1 , . . , Nn ) such that ˚ X(0, 0) = X, Xui (0, 0) = Z˚(i) , Nσ (0, 0) = N˚ σ . t. to the ONF N, and the Tσϑ,i ≡ Tσϑ,i represent the respective torsion coefficients. Our proof of this theorem follows the lines of Blaschke and Leichtweiss [15]. Preceded is the following lemma (see also ibidem, § 60). 1. Consider the initial value problem m ∂ zk = ∑ aℓki zℓ , i ∂u ℓ=1 zk (u0 , v0 ) = z˚k , i = 1, 2, k = 1, .

6 The Weingarten equations 31 Proof. With unknown functions aσ ,i and bσϑ ,i we evaluate the ansatz Nσ ,ui = 2 n k=1 ϑ =1 ∑ akσ ,iXuk + ∑ bσϑ ,i Nϑ . Multiplication by Xuℓ gives −Lσ ,iℓ = Nσ ,ui · Xuℓ = 2 2 k=1 k=1 ∑ akσ ,i Xuk · Xuℓ = ∑ akσ ,igkℓ , and rearranging yields 2 ℓm am σ ,i = − ∑ Lσ ,iℓ g . ℓ=1 A further multiplication by Nω shows Tσω,i = Nσ ,ui · Nω = n n ϑ =1 ϑ =1 ∑ bσϑ ,i Nϑ · Nω = ∑ bσϑ ,iδϑ ω = bσω,i , which proves the statement. 11) generalizes the classical Weingarten equations 2 Nui = − ∑ Li j g jk Xuk , i = 1, 2, j,k=1 for the unit normal vector N of a surface X : B → Rn+2 in the case of one codimension n = 1, found by the German mathematician Julius Weingarten (*1836 in Berlin; †1910 in Freiburg).

There is an endless list of contemporary studies on constant mean curvature surfaces. The reader finds various excellent contributions in the works of U. Abresch, B. Ammann, C. Gerhardt, K. Grosse-Brauckmann, F. Helein, J. Isenberg, H. Karcher, M. Kilian, K. Kenmotsu, N. Kapouleas, R. Lopez, R. Kusner, F. H. Meeks, F. Pedit, K. Polthier, N. Schmidt, J. Sullivan, M. Weber, H. Wente etc. In 1972, David Hoffman in [92] considered the embedding problem for compact surfaces with parallel mean curvature vector in four-dimensional Euclidean space.

Download PDF sample

Rated 4.95 of 5 – based on 41 votes