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 Kontsevich-Zagier 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 long-standing 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 self-contained.

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 Kontsevich-Zagier 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 long-standing 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 self-contained.

Friedrich Jonas' zweibandige Geschichte der Soziologie bietet einen fundierten ideengeschichtlichen UEberblick uber die Vorlaufer, die Entstehung und den Verlauf der Soziologie im internationalen Kontext. Im ersten Band werden die zentralen Gesellschaftslehren in der Aufklarung, im Idealismus, Liberalismus, Sozialismus und Positivismus dargestellt und eroertert. Im zweiten Band werden die geistesgeschichtlichen Entwicklungen der Soziologie in einzelnen Landern vorgestellt. Dadurch entsteht ein beeindruckender UEberblick uber die Geschichte der soziologischen Denkweisen in Mitteleuropa und den USA, getreu Friedrich Jonas' Motto: "Die Geschichte der Soziologie hoert nicht auf, wenn das jeweils letzte Kapitel zu Ende geschrieben ist. [...] Als begriffene Geschichte ist sie die Quelle der Erneuerung und Lebendigkeit, ohne die die Wissenschaft nur ein kraftloser und irrelevanter Schatten ihrer selbst ware."

Friedrich Jonas' zweibandige Geschichte der Soziologie bietet einen fundierten ideengeschichtlichen UEberblick uber die Vorlaufer, die Entstehung und den Verlauf der Soziologie im internationalen Kontext. Im ersten Band werden die zentralen Gesellschaftslehren in der Aufklarung, im Idealismus, Liberalismus, Sozialismus und Positivismus dargestellt und eroertert. Im zweiten Band werden die geistesgeschichtlichen Entwicklungen der Soziologie in einzelnen Landern vorgestellt. Dadurch entsteht ein beeindruckender UEberblick uber die Geschichte der soziologischen Denkweisen in Mitteleuropa und den USA, getreu Friedrich Jonas' Motto: "Die Geschichte der Soziologie hoert nicht auf, wenn das jeweils letzte Kapitel zu Ende geschrieben ist. [...] Als begriffene Geschichte ist sie die Quelle der Erneuerung und Lebendigkeit, ohne die die Wissenschaft nur ein kraftloser und irrelevanter Schatten ihrer selbst ware."