The resulting category is a natural target for the direct image map from the category of Hermitian sheaves on an Arakelov variety. The morphisms are linear maps that are non-expanding with respect to both functions, and our objects are formal quotients of two Euclidean spaces. The main object at infinity is, roughly speaking, a pair of positive quadratic functions on a real vector space, one greater than the other. We propose a natural, and essentially elementary, construction, that has the potential to greatly enhance Arakelov Geometry in several ways. The main obstacle to generalizing this analogy to coherent sheaves is to understand what to do at infinity.
It is well-known that lattices in Euclidean spaces are arithmetic analogs of locally free sheaves over the compactified spectrum of the ring of integers. November 30 Speaker: Alexander Borisov (Binghamton) Title: Bi-Euclidean spaces and coherent sheaves on Arakelov curves, Part 2 Abstract: This will be a continuation (with some repetition) of the talk from October 5. Dogs spontaneously process basic numerical quantities, using a distinct part of their brains that corresponds closely to number-responsive neural regions in. Related seminar: The student/postdoc “No Theory Seminar”: Only Basic Number Theory (Die Grundlehren Der Mathematischen Wissenschaften In Einzeldarstellungen) Andre Weil 1.99/ Month for Unlimited Devices.
Related seminar: Upstate New York Online Number Theory Colloquium (bi-weekly, online): SEMINAR ANNOUNCEMENTS: To receive announcements of seminar talks by email, please join our mailing list. Patrick Milano (May 2018), Changwei Zhou (May 2019). students (in number theory and related topics): Ilir Snopce (Dec. students: Patrick Carney, Andrew Lamoureux, Micah Loverro, and Sayak Sengupta. ORGANIZERS: Regular Faculy: Alexander Borisov, Marcin Mazur, Adrian Vasiu, Post-Docs: Sailun Zhan,Ĭurrent Ph.D. The in-house talks will be in-person, while visitors outside of Binghamton area will be by Zoom: Zoom link PLACE and TIME: This semester the seminar meets primarily on Tuesdays at 4:15 p.m, with possible special lectures on Mondays at 3:30 or other days and times. TOPICS: Arithmetic in the broadest sense that includes Number Theory (Elementary Arithmetic, Algebraic, Analytic, Combinatorial, etc.), Algebraic Geometry, Representation Theory, Lie Groups and Lie Algebras, Diophantine Geometry, Geometry of Numbers, Tropical Geometry, Arithmetic Dynamics, etc.