Nikita Karpenko's Books

The Algebraic and Geometric Theory of Quadratic Forms

By: Richard S. Elman,Nikita Karpenko,Alexander Merkurjev

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The Algebraic and Geometric Theory of Quadratic Forms

By: Richard S. Elman,Nikita Karpenko,Alexander Merkurjev

This book is a comprehensive study of the algebraic theory of quadratic forms, from classical theory to recent developments, including results and proofs that have never been published. The book is written from the viewpoint of algebraic geometry and includes the theory of quadratic forms over fields of characteristic two, with proofs that are characteristic independent whenever possible. For some results both classical and geometric proofs are given. Part I includes classical algebraic theory of quadratic and bilinear forms and answers many questions that have been raised in the early stages of the development of the theory. Assuming only a basic course in algebraic geometry, Part II presents the necessary additional topics from algebraic geometry including the theory of Chow groups, Chow motives, and Steenrod operations. These topics are used in Part III to develop a modern geometric theory of quadratic forms.

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Page Count

456

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821873229

ISBN 13

9780821873229

Geometric Methods in the Algebraic Theory of Quadratic Forms

Summer School, Lens, 2000

By: Oleg T. Izhboldin,Bruno Kahn,Nikita A. Karpenko,Alexander Vishik

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Geometric Methods in the Algebraic Theory of Quadratic Forms

Summer School, Lens, 2000

By: Oleg T. Izhboldin,Bruno Kahn,Nikita A. Karpenko,Alexander Vishik

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes an introduction to motives of quadrics by A. Vishik, with various applications, notably to the splitting patterns of quadratic forms, papers by O. Izhboldin and N. Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields with u-invariant 9, and a contribution in French by B. Kahn which lays out a general framework for the computation of the unramified cohomology groups of quadrics and other cellular varieties.

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Page Count

198

Publisher

Springer

Published Date

ISBN 10

3540409904

ISBN 13

9783540409908

Vibrational (Infrared and Raman) Spectra of Minerals and Related Compounds

By: Nikita V. Chukanov,Marina F. Vigasina

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Vibrational (Infrared and Raman) Spectra of Minerals and Related Compounds

By: Nikita V. Chukanov,Marina F. Vigasina

The book presents new data on the IR spectra of minerals and on the Raman spectra of more than 2000 mineral species. It also includes examples of IR spectroscopy applications to investigate minerals, and discusses the most important potential applications of Raman spectroscopy in mineralogical research. The book serves as a reference resource and a methodological guide for mineralogists, petrologists and technologists working in the field of inorganic materials.

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Page Count

1382

Publisher

Springer Nature

Published Date

ISBN 10

3030268039

ISBN 13

9783030268039

Infrared spectra of mineral species

Extended library

By: Nikita V. Chukanov

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Infrared spectra of mineral species

Extended library

By: Nikita V. Chukanov

Over the last 30 years, Dr. Nikita V. Chukanov has collected IR spectra of about 2000 mineral species, including 247 holotype samples. In this book, he presents 3309 spectra of these minerals with detailed description and analytical data for reference samples. In the course of this work, about 150 new mineral species have been discovered. After an introductory chapter, infrared spectra of minerals are given together with the descriptions of standard samples used (occurrence, appearance, associated minerals, empirical formula etc.) and some comments. Sections are organized according to different classes of compounds (silicates, phosphates, arsenates, oxides etc.).

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1733

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9400771282

ISBN 13

9789400771284

Infrared Spectroscopy of Minerals and Related Compounds

By: Nikita V. Chukanov,Alexandr D. Chervonnyi

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Infrared Spectroscopy of Minerals and Related Compounds

By: Nikita V. Chukanov,Alexandr D. Chervonnyi

This book provides an overview of the application of IR spectroscopy in mineralogical investigations, as well as modern trends in the IR spectroscopy of minerals. It includes the most important methodological aspects; characteristic IR bands of different chemical groups and coordination polyhedra; application of IR spectroscopy to the investigation of the crystal chemistry of amphiboles, phyllosilicates, tourmalines etc.; neutral molecules entrapped by microporous minerals; and analysis of hydrogen in nominally anhydrous minerals. About 1600 IR spectra (illustrations as well as a list of wavenumbers) of minerals and some related compounds are accompanied by detailed descriptions of the standard samples used. Each spectrum provides information about the occurrence, appearance, associated minerals, its empirical formula, and unit-cell parameters. The book also provides insights into sample preparation and/or spectrum registration methods. It includes IR spectra of 1020 minerals that were not covered in the book “Infrared spectra of mineral species: Extended library” published in 2014 and written by one of the authors. On average, each page provides information on two minerals/compounds. Subsections correspond to different classes of compounds (silicates, phosphates, arsenates, oxides etc.). About 290 new spectra have been obtained, and the remaining 1310 spectra are taken from most reliable literature sources (published over the last 60 years) and are redrawn in a unified style.

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Page Count

1117

Publisher

Springer

Published Date

ISBN 10

3319253492

ISBN 13

9783319253497

Geometric Methods in the Algebraic Theory of Quadratic Forms

Summer School, Lens, 2000

By: Oleg T. Izhboldin,Bruno Kahn,Nikita A. Karpenko,Alexander Vishik

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Geometric Methods in the Algebraic Theory of Quadratic Forms

Summer School, Lens, 2000

By: Oleg T. Izhboldin,Bruno Kahn,Nikita A. Karpenko,Alexander Vishik

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Solve jigsaw puzzle

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Page Count

198

Publisher

Springer

Published Date

ISBN 10

3540409904

ISBN 13

9783540409908

Book's by Nikita Karpenko

The Algebraic and Geometric Theory of Quadratic Forms

The Algebraic and Geometric Theory of Quadratic Forms

Geometric Methods in the Algebraic Theory of Quadratic Forms

Geometric Methods in the Algebraic Theory of Quadratic Forms

Vibrational (Infrared and Raman) Spectra of Minerals and Related Compounds

Vibrational (Infrared and Raman) Spectra of Minerals and Related Compounds

Infrared spectra of mineral species

Infrared spectra of mineral species

Infrared Spectroscopy of Minerals and Related Compounds

Infrared Spectroscopy of Minerals and Related Compounds

Geometric Methods in the Algebraic Theory of Quadratic Forms

Geometric Methods in the Algebraic Theory of Quadratic Forms

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