Martin Olsson

• Inflation, ras på annonsmarknaden och ökade kostnader på alla områden har slagit hårt mot mediebranschen 2023. • Tappet på annonsmarknaden är det kraftigaste sedan finanskrisen 2009 och en central förklaring till den ekonomiska krisen. • Antalet lokalredaktioner är i princip oförändrat jämfört med förra året. Samtidigt skapar den pressade ekonomin oro inför 2024. • Krig, desinformation och propaganda ställer nya krav på mediernas källkritik och etiska kompass. • Årets snackis är artificiell intelligens – påverkar det journalistiken? Det är några av de tydligaste trenderna för den svenska journalistiken som tecknas i Mediestudiers årsbok 2023.

A pioneering new nonlinear approach to a fundamental question in algebraic geometryOne of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates, up to a linear ambiguity. What Determines an Algebraic Variety? develops a nonlinear version of this theory, offering the first nonlinear generalization of the seminal work of Veblen and Young in a century. While the book uses cutting-edge techniques, the statements of its theorems would have been understandable a century ago; despite this, the results are totally unexpected. Putting geometry first in algebraic geometry, the book provides a new perspective on a classical theorem of fundamental importance to a wide range of fields in mathematics. Starting with basic observations, the book shows how to read off various properties of a variety from its geometry. The results get stronger as the dimension increases. The main result then says that a normal projective variety of dimension at least 4 over a field of characteristic 0 is completely determined by its Zariski topological space. There are many open questions in dimensions 2 and 3, and in positive characteristic.

A pioneering new nonlinear approach to a fundamental question in algebraic geometryOne of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates, up to a linear ambiguity. What Determines an Algebraic Variety? develops a nonlinear version of this theory, offering the first nonlinear generalization of the seminal work of Veblen and Young in a century. While the book uses cutting-edge techniques, the statements of its theorems would have been understandable a century ago; despite this, the results are totally unexpected. Putting geometry first in algebraic geometry, the book provides a new perspective on a classical theorem of fundamental importance to a wide range of fields in mathematics. Starting with basic observations, the book shows how to read off various properties of a variety from its geometry. The results get stronger as the dimension increases. The main result then says that a normal projective variety of dimension at least 4 over a field of characteristic 0 is completely determined by its Zariski topological space. There are many open questions in dimensions 2 and 3, and in positive characteristic.

• Redaktionsdöden i landets kommuner har stannat av. Däremot fortsätter ägarkoncentrationen att öka. • Trots att reklamintäkterna till journalistik gjorde en historisk återhämtning efter pandemin, ser framtiden dyster ut. • Konsumenterna efterfrågar journalistik och är villiga att betala för den. Inte minst hos yngre finns det en betalningsvilja på nätet. • Förslaget till nytt mediestöd kan innebära en radikal förändring, där vinnarna troligen blir mindre lokala aktörer, både i form av etablerade, tryckta medier och nyare, enbart digitala sådana. Det är några av de tydligaste trenderna för den svenska journalistiken som tecknas i Mediestudiers årsbok 2022. Läget för den lokala journalistiken i varje kommun finns på: https://kommundatabas.mediestudier.se/

This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curves. Numerous exercises are included in each chapter ranging from routine verifications to more difficult problems, and a glossary of necessary category theory is included as an appendix.