Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
3,136
result(s) for
"Algebraic spaces."
Sort by:
Cancellation for Surfaces Revisited
The celebrated Zariski Cancellation Problem asks as to when the existence of an isomorphism
If the cancellation does not hold then
eBook
Algebraic geometry over C∞-rings
If X is a manifold then the \\mathbb R-algebra C^\\infty (X) of smooth functions c:X\\rightarrow \\mathbb R is a C^\\infty -ring. That is, for each smooth function f:\\mathbb R^n\\rightarrow \\mathbb R there is an n-fold operation \\Phi _f:C^\\infty (X)^n\\rightarrow C^\\infty (X) acting by \\Phi _f:(c_1,\\ldots ,c_n)\\mapsto f(c_1,\\ldots ,c_n), and these operations \\Phi _f satisfy many natural identities. Thus, C^\\infty (X) actually has a far richer structure than the obvious \\mathbb R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C^\\infty -rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C^\\infty -schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C^\\infty -schemes, and C^\\infty -stacks, in particular Deligne-Mumford C^\\infty-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C^\\infty-rings and C^\\infty -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, \"derived\" versions of manifolds and orbifolds related to Spivak's \"derived manifolds\".
eBook
Topological Complexity and Related Topics
This volume contains the proceedings of the mini-workshop on Topological Complexity and Related Topics, held from February 28-March 5, 2016, at the Mathematisches Forschungsinstitut Oberwolfach. Topological complexity is a numerical homotopy invariant, defined by Farber in the early twenty-first century as part of a topological approach to the motion planning problem in robotics. It continues to be the subject of intensive research by homotopy theorists, partly due to its potential applicability, and partly due to its close relationship to more classical invariants, such as the Lusternik-Schnirelmann category and the Schwarz genus. This volume contains survey articles and original research papers on topological complexity and its many generalizations and variants, to give a snapshot of contemporary research on this exciting topic at the interface of pure mathematics and engineering.
eBook
Topology, Geometry, and Dynamics
Vladimir Abramovich Rokhlin (8/23/1919-12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory.The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19-23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia.The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.
eBook
Introduction to Ramsey Spaces
Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite.
eBook
Modular forms
This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it.
eBook