MüllerStach, Stefan 1962
Overview
Works:  22 works in 66 publications in 2 languages and 1,142 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA564, 516.35 
Publication Timeline
.
Most widely held works by
Stefan MüllerStach
Period mappings and period domains by
James A Carlson(
Book
)
10 editions published between 2003 and 2017 in English and held by 228 WorldCat member libraries worldwide
The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a twotorus varies, thereby showing that certain families contain all elliptic curves. Generalizing to higher dimensions resulted in the formulation of the celebrated Hodge conjecture, and in an attempt to solve this, Griffiths generalized the classical notion of period matrix and introduced period maps and period domains which reflect how the complex structure for higher dimensional varieties varies. The basic theory as developed by Griffiths is explained in the first part of the book. Then, in the second part spectral sequences and Koszul complexes are introduced and are used to derive results about cycles on higher dimensional algebraic varieties such as the NoetherLefschetz theorem and Nori's theorem. Finally, in the third part differential geometric methods are explained leading up to proofs of Arakelovtype theorems, the theorem of the fixed part, the rigidity theorem, and more. Higgs bundles and relations to harmonic maps are discussed, and this leads to striking results such as the fact that compact quotients of certain period domains can never admit a Kahler metric or that certain lattices in classical Lie groups can't occur as the fundamental group of a Kahler manifold
10 editions published between 2003 and 2017 in English and held by 228 WorldCat member libraries worldwide
The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a twotorus varies, thereby showing that certain families contain all elliptic curves. Generalizing to higher dimensions resulted in the formulation of the celebrated Hodge conjecture, and in an attempt to solve this, Griffiths generalized the classical notion of period matrix and introduced period maps and period domains which reflect how the complex structure for higher dimensional varieties varies. The basic theory as developed by Griffiths is explained in the first part of the book. Then, in the second part spectral sequences and Koszul complexes are introduced and are used to derive results about cycles on higher dimensional algebraic varieties such as the NoetherLefschetz theorem and Nori's theorem. Finally, in the third part differential geometric methods are explained leading up to proofs of Arakelovtype theorems, the theorem of the fixed part, the rigidity theorem, and more. Higgs bundles and relations to harmonic maps are discussed, and this leads to striking results such as the fact that compact quotients of certain period domains can never admit a Kahler metric or that certain lattices in classical Lie groups can't occur as the fundamental group of a Kahler manifold
Transcendental aspects of algebraic cycles : proceedings of the Grenoble Summer School, 2001 by
Stefan MüllerStach(
Book
)
13 editions published in 2004 in English and held by 218 WorldCat member libraries worldwide
Topics range from introductory lectures on algebraic cycles to more advanced material in this collection of lecture notes from the Proceedings of the Grenoble Summer School, 2001. The advanced lectures are grouped under three headings: Lawson (co)homology, motives and motivic cohomology and Hodge theoretic invariants of cycles. As the lectures were intended for nonspecialists, many examples have been included
13 editions published in 2004 in English and held by 218 WorldCat member libraries worldwide
Topics range from introductory lectures on algebraic cycles to more advanced material in this collection of lecture notes from the Proceedings of the Grenoble Summer School, 2001. The advanced lectures are grouped under three headings: Lawson (co)homology, motives and motivic cohomology and Hodge theoretic invariants of cycles. As the lectures were intended for nonspecialists, many examples have been included
Elementare und algebraische Zahlentheorie : ein moderner Zugang zu klassischen Themen by
Stefan MüllerStach(
Book
)
12 editions published between 2006 and 2011 in German and held by 127 WorldCat member libraries worldwide
Das Buch wendet sich an alle, die in die klassischen Themen der Zahlentheorie einsteigen wollen. Neben den Standardthemen wie Primzahlen, Rechnen modulo n, quadratische Reste und Kettenbrüche werden auch die fortgeschrittenen Bereiche wie padische Zahlen, quadratische Formen und Zahlkörper am Beispiel der quadratischen Zahlkörper behandelt. Viel Wert wird auf die konkrete Berechenbarkeit bei allen Problemlösungen gelegt. So gibt es auch Abschnitte über moderne Primzahltests und Faktorisierungsalgorithmen und am Ende des Buches wird ein Weg zur Bestimmung der Klassenzahl der quadratischen Zahlkörper aufgezeigt. Im Rahmen der Bachelor/MasterStudiengänge eignet sich das Buch als Grundlage für zwei Semester: ein Aufbaumodul in elementarer Zahlentheorie mit einem Vertiefungsmodul in algebraischer Zahlentheorie
12 editions published between 2006 and 2011 in German and held by 127 WorldCat member libraries worldwide
Das Buch wendet sich an alle, die in die klassischen Themen der Zahlentheorie einsteigen wollen. Neben den Standardthemen wie Primzahlen, Rechnen modulo n, quadratische Reste und Kettenbrüche werden auch die fortgeschrittenen Bereiche wie padische Zahlen, quadratische Formen und Zahlkörper am Beispiel der quadratischen Zahlkörper behandelt. Viel Wert wird auf die konkrete Berechenbarkeit bei allen Problemlösungen gelegt. So gibt es auch Abschnitte über moderne Primzahltests und Faktorisierungsalgorithmen und am Ende des Buches wird ein Weg zur Bestimmung der Klassenzahl der quadratischen Zahlkörper aufgezeigt. Im Rahmen der Bachelor/MasterStudiengänge eignet sich das Buch als Grundlage für zwei Semester: ein Aufbaumodul in elementarer Zahlentheorie mit einem Vertiefungsmodul in algebraischer Zahlentheorie
Periods and Nori motives by
Annette Huber(
Book
)
7 editions published in 2017 in English and held by 41 WorldCat member libraries worldwide
"This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of KontsevichZagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are longstanding conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori's unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is selfcontained."Provided by publisher
7 editions published in 2017 in English and held by 41 WorldCat member libraries worldwide
"This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of KontsevichZagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are longstanding conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori's unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is selfcontained."Provided by publisher
Crashkurs Hodgetheorie by
Stefan MüllerStach(
Book
)
1 edition published in 1994 in German and held by 15 WorldCat member libraries worldwide
1 edition published in 1994 in German and held by 15 WorldCat member libraries worldwide
The arithmetic and geometry of algebraic cycles by
B. Brent Gordon(
Book
)
2 editions published in 2000 in English and held by 7 WorldCat member libraries worldwide
The subject of algebraic cycles has thrived through its interaction with algebraic Ktheory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic Ktheory, the arithmetic AbelJacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. <br/> The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. <br/> This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and Ktheory methods. Topics include a discussion of the arithmetic AbelJacobi mapping, higher AbelJacobi regulator maps, polylogarithms and Lseries, candidate BlochBeilinson filtrations, applications of ChernSimons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties
2 editions published in 2000 in English and held by 7 WorldCat member libraries worldwide
The subject of algebraic cycles has thrived through its interaction with algebraic Ktheory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic Ktheory, the arithmetic AbelJacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. <br/> The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. <br/> This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and Ktheory methods. Topics include a discussion of the arithmetic AbelJacobi mapping, higher AbelJacobi regulator maps, polylogarithms and Lseries, candidate BlochBeilinson filtrations, applications of ChernSimons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties
Zahlentheorie(
Book
)
1 edition published in 2006 in German and held by 4 WorldCat member libraries worldwide
1 edition published in 2006 in German and held by 4 WorldCat member libraries worldwide
L2vanishing theorems on ball quotients and applications by
Stefan MüllerStach(
Book
)
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
The MilnorChow homomorphism revisited by
Moritz Kerz(
Book
)
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
Polylogarithmic identities in cubical higher chow groups by
Herbert Gangl(
Book
)
2 editions published between 1997 and 1998 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1997 and 1998 in English and held by 3 WorldCat member libraries worldwide
Compactifications of C 3 with reducible boundary divisor by
Stefan MüllerStach(
Book
)
1 edition published in 1989 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 2 WorldCat member libraries worldwide
The Arithmetic and Geometry of Algebraic Cycles by
B. Brent Gordon(
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Algebraic cycles on certain CalabiYau threefolds by
F Bardelli(
Book
)
2 editions published in 1992 in English and held by 1 WorldCat member library worldwide
2 editions published in 1992 in English and held by 1 WorldCat member library worldwide
Eine Anwendung der Klassifikationstheorie projektiver Varietäten auf Kompaktifizierungen des C_1hn3 [C] by
Stefan MüllerStach(
Book
)
1 edition published in 1989 in German and held by 1 WorldCat member library worldwide
1 edition published in 1989 in German and held by 1 WorldCat member library worldwide
Syzygies and the AbelJacobi map for cyclic coverings by
Stefan MüllerStach(
Book
)
1 edition published in 1993 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1993 in Undetermined and held by 1 WorldCat member library worldwide
Otto Toeplitz: Algebraiker der unendlichen Matrizen : eine schmerzvolle Liebe zu Deutschland by
Stefan MüllerStach(
)
1 edition published in 2014 in German and held by 1 WorldCat member library worldwide
1 edition published in 2014 in German and held by 1 WorldCat member library worldwide
Periods and Nori Motives by
Annette Huber(
)
1 edition published in 2017 in German and held by 0 WorldCat member libraries worldwide
1 edition published in 2017 in German and held by 0 WorldCat member libraries worldwide
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Related Identities
 Peters, C. (Chris) Other Editor
 Piontkowski, Jens
 Carlson, James A. 1946 Author
 Huber, Annette Author
 Gordon, B. Brent Author Editor
 Lewis, James D. Editor
 Piontkowski, Jens
 Yui, Noriko
 Saito, Shuji
 Friedrich, Benjamin Collector Contributor
Useful Links
Alternative Names
MüllerStach, S.
MüllerStach, S. 1962
MüllerStach, S. J. 1962
MüllerStach, S. (Stefan), 1962
MüllerStach, St 1962
MüllerStach, St. J. 1962
MüllerStach, Stefan
MüllerStach, Stefan J. 1962
Stach, Stefan Müller.
Stach, Stefan Müller 1962...
Stefan MüllerStach Duits wiskundige
Stefan MüllerStach German mathematician
Stefan MüllerStach matemático alemán
Stefan MüllerStach mathématicien allemand
Stefan MüllerStach tysk matematikar
Stefan MüllerStach tysk matematiker
اشتفان مولراشتاخ ریاضیدان آلمانی
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