Height functions for motives, II
نویسندگان
چکیده
This is the Part II of our paper “Height functions for motives”. We consider more general period domains and height on sets motives. also corresponding Hodge theoretic variant Nevanlinna theory.
منابع مشابه
Motives : Motivic L - functions
The exposition here follows the lecture delivered at the summer school, and hence, contains neither precision, breadth of comprehension, nor depth of insight. The goal rather is the curious one of providing a loose introduction to the excellent introductions that already exist, together with scattered parenthetical commentary. The inadequate nature of the exposition is certainly worst in the th...
متن کاملHeight Functions
Definition 1. An (archimedean) absolute value on a field k is a real valued function ‖ · ‖ : k → [0,∞) with the following three properties: (1) ‖x‖ = 0 if and only if x = 0. (2) ‖xy‖ = ‖x‖ · ‖y‖. (3) ‖x+ y‖ ≤ ‖x‖+ ‖y‖. A nonarchimedean absolute value satisfies the extra condition that (3’) ‖x+ y‖ ≤ max{‖x‖, ‖y‖}. If k is a field, we denote Mk the set of absolute values on k. As an abuse of nota...
متن کاملCategories of Motives for Additive Categories. Ii
This is a continuation of the paper by the same author published in this journal, v. 19 (2007), no. 6. This paper is a continuation of the paper [4] and makes a whole with it. We retain the notation, the definitions, and the assumptions of [4], and we continue the numeration of sections, theorems and lemmas. The proofs of Theorems 2–4 in §6 of [4] were in fact missing; it was said only that one...
متن کاملMotives and Motivic L-functions
This report aims to be an exposition of the theory of L-functions from the motivic point of view. The classical theory of pure motives provides a category consisting of ‘universal cohomology theories’ for smooth projective varieties defined over – for instance – number fields. Attached to every motive we can define a function which is holomorphic on a subdomain of C which at least conjecturally...
متن کاملMotivic Zeta Functions of Motives
LetM be a tensor category with coefficients in a fieldK of characteristic 0, that is, a K-linear pseudo-abelian symmetric monoidal category such that the tensor product ⊗ of M is bilinear. Then symmetric and exterior powers of an object M ∈ M make sense, by using appropriate projectors relative to the action of the symmetric groups on tensor powers of M . One may therefore introduce the zeta fu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advanced studies in pure mathematics
سال: 2021
ISSN: ['2433-8915', '0920-1971']
DOI: https://doi.org/10.2969/aspm/08610467