Arithmetic, K-Theory, and Algebraic Cycles

This proceedings volume gathers peer-reviewed works presented at the "Arithmetic, K-Theory, and Algebraic Cycles" international conference held at Ohio State University, USA, from May 27-31, 2025. Papers in this volume cover cutting-edge aspects of these theories, offering a snapshot of leading research in arithmetic and algebraic geometry, K-theory, and algebraic cycles. Contributions were submitted by researchers from the Americas, Europe, and Asia, with participation mostly in person. As a result of fertile cooperation between renowned researchers in the field and junior researchers, this volume will be of special appeal to both experienced mathematicians and graduate students seeking new avenues of research. Inhaltsverzeichnis Chapter 1 Tame and Curve-tame cohomology of ${\mathbb A}^1$ invariant \'etale sheaves.- Chapter 2 Zero cycles on bi-elliptic surfaces.- Cahpter 3 The Motivic and \'Etale Becker-Gottlieb transfer: the construction of the transfer.- Cahpter 4 The Motivic and \'Etale Becker-Gottlieb transfer and splittings.- Cahpter 5 Some remarks on Chow correspondences.- Chapter 6 Elementary interactions between line bundles, algebraic cycles and gerbes.- Chapter 7 Brauer groups of smooth split toric schemes and their fans.- Cahpter 8 Brauer groups of Horospherical varieties.- Chapter 9 On presentations of K-groups by generators and relations.- Chapter 10 Three vignettes on hypergeometric normal functions. Autorenportrait Roy Joshua is a full professor at the Ohio State University, USA. His research fields are algebraic geometry, K-theory, and arithmetic geometry. He has published over 46 papers in leading journals in his field. Patrick Brosnan is a full professor at the University of Maryland, College Park, USA. He currently works in algebraic geometry and has a number of publications in leading journals in his field. Connor Cassady is a visiting assistant professor at Colgate University. He received his PhD in Mathematics (2023) from the University of Pennsylvania under the supervision of Dr. David Harbater and was an Assistant Professor at the Ohio State University from August, 2023 through May, 2026.