"Ce travail est consacré à la découverte, la définition et l'étude de la courbe fondamentale en théorie de Hodge p-adique. On prend pour cela le point de vue de définir et d'étudier les différents anneaux de périodes p-adiques comme anneaux de fonctions holomorphes de la variabl…
"This book investigates, roughly speaking, the variation of the properties of the fibers of a map between analytic spaces in the sense of Berkovich. First of all, we study flatness in this setting; the naive definition of this notion is not reasonable, we explain why and give an…
The systole of a compact metric space $X$ is a metric invariant of $X$, defined as the least length of a noncontractible loop in $X$. When $X$ is a graph, the invariant is usually referred to as the girth, ever since the 1947 article by W. Tutte. The first nontrivial results for…
Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of mathematics that started in the eighteen hundreds. Century-old problems of enumerating geometric c…
A text for a year-long introduction to arithmetic geometry, leading the reader in a logical progression from the local to the global properties of rings and curves through the study of class groups and of the Riemann-Roch theorem. Emphasizes the connection between algebraic numb…
"Moduli problems in algebraic geometry date back to Riemann's famous count of the 3g - 3 parameters needed to determine a curve of genus g. In this book, Zariski studies the moduli space of curves of the same equisingularity class."--Jacket.
Relative p-adic Hodge theory: foundations
by Kedlaya, Kiran Sridhara, Liu, Ruochuan
fromAstérisque
"We describe a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. We give a thorough development of [phi]-modules over a relative Robba ring associated t…
" ... Les thèmes abordés reflètent la diversité et la richesse des travaux et des centres d'intérêt de Gérard Laumon : cohomologie étale des schémas et des champs, faisceaux -adiques et transformation de Fourier, faisceaux caractères, correspondance de Langlands classique et géo…
On the derived category of 1-motives
by Barbieri-Viale, Luca, Kahn, Bruno
fromAstérisque
Instanton moduli spaces and W-algebras
by Braverman, Alexander, Finkelberg, Michael, Nakajima, Hiraku
fromAstérisque
We describe the (equivariant) intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g., the Poincaré pairing) in terms of representation theory of some vertex operator algebras ("W-algebras").
"This work applies Gabber's theorem on alterations to Veovodsky's work on mixed motives ... Two applications are an isomorphism to Suslin that compares higher Chow groups and étale cohomology, and calculation of the motivic Steenrod algebra"--Back cover.
