Tropical geometry over higher dimensional local fields
نویسندگان
چکیده
منابع مشابه
The Bruhat – Tits buildings over higher dimensional local fields
A generalization of the Bruhat–Tits buildings for the groups PGL(V ) over n-dimensional local fields was introduced in [P1]. The main object of the classical Bruhat–Tits theory is a simplicial complex attached to any reductive algebraic group G defined over a field K . There are two parallel theories in the case where K has no additional structure or K is a local (or more generally, complete di...
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Suppose that we are given a surface S over a finite field of characteristic p, a curve C ⊂ S , and a point x ∈ C such that both S and C are regular at x. Then one can attach to these data the quotient field of the completion ̂ (ÔS,x)C of the localization at C of the completion ÔS,x of the local ring OS,x of S at x. This is a two-dimensional local field over a finite field, i.e., a complete discr...
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The paper contains a construction of ramification theory for higher dimensional local fields K provided with additional structure given by an increasing sequence of their “subfields of i-dimensional constants”, where 0 i n and n is the dimension of K. It is also announced that a local analogue of the Grothendieck Conjecture still holds: all automorphisms of the absolute Galois group of K, which...
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Example. Let X be an algebraic projective irreducible surface over a field k and let P be a closed point of X , C ⊂ X be an irreducible curve such that P ∈ C . If X and C are smooth at P , then we let t ∈ OX,P be a local equation of C at P and u ∈ OX,P be such that u|C ∈ OC,P is a local parameter at P . Denote by C the ideal defining the curve C near P . Now we can introduce a two-dimensional l...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2015
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2012-0124