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Abstrak :
This book provides a rapid introduction to complex algebraic geometry. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. It combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas.

Abstrak :
This book contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics. The problems are clustered by topic into three self-contained chapters. The book begins with elementary facts, followed by carefully selected problems and detailed, step-by-step solutions, which then lead to more complicated, challenging problems and their solutions. Reflecting the vast experience of two professors and mathematical olympiad coaches.

Abstrak :
This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. New results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.

Abstrak :
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and laplace and seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text.

Abstrak :
Aims at uniting maximal orders, valuation rings, Dubrovin valuations, and more in a common theory, the theory of primes of algebras. This title also establishes possible applications of the noncommutative arithmetics to interesting classes of algebras

Abstrak :
This book acknowledges the varied incarnations of the fundemental group, pro-finite, L-adic, p-adic, pro-algebraic and motivic. It explores a weaelth of topics that range from anabelian geometry (in particular the section conjecture), the L-adic polylogarithm, gonality questions of mudular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's nonabelian Chaubauty method and p-adic integration after Coleman.

Abstrak :
This book is about modern algebraic geometry. The book starts by explaining this enigmatic answer, algebraic geometry. From a point of departure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendieck’s theory of schemes. Contemporary homological tools are explained.

Abstrak :
This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.