Tame degree functions in arbitrary characteristic

2021 ◽  
Vol 225 (10) ◽  
pp. 106715
Author(s):  
Neena Gupta ◽  
Sourav Sen
Keyword(s):  
Arbitrary Characteristic

scholarly journals A remark on the Grothendieck-Lefschetz theorem about the Picard group

1978 ◽  
Vol 71 ◽  
pp. 169-179 ◽  
Author(s):  
Lucian Bădescu
Keyword(s):  
Algebraic Variety ◽  
Picard Group ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Arbitrary Characteristic ◽  
Lefschetz Theorem

Let K be an algebraically closed field of arbitrary characteristic. The term “variety” always means here an irreducible algebraic variety over K. The notations and the terminology are borrowed in general from EGA [4].

scholarly journals Connected fields of arbitrary characteristic

1966 ◽  
Vol 5 (2) ◽  
pp. 177-184 ◽  
Author(s):  
Alan G. Waterman ◽  
George M. Bergman
Keyword(s):  
Arbitrary Characteristic

scholarly journals The number of idempotents in abelian group rings

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 719-723
Author(s):  
Peter Danchev
Keyword(s):  
Abelian Group ◽  
Group Ring ◽  
Group Rings ◽  
Arbitrary Characteristic

Suppose that R is a commutative unitary ring of arbitrary characteristic and G is a multiplicative abelian group. Our main theorem completely determines the cardinality of the set id(RG), consisting of all idempotent elements in the group ring RG. It is explicitly calculated only in terms associated with R, G and their divisions. This result strengthens previous estimates obtained in the literature recently.

scholarly journals A COMPUTABLE FUNCTOR FROM GRAPHS TO FIELDS

2018 ◽  
Vol 83 (1) ◽  
pp. 326-348 ◽  
Author(s):  
RUSSELL MILLER ◽  
BJORN POONEN ◽  
HANS SCHOUTENS ◽  
ALEXANDRA SHLAPENTOKH
Keyword(s):  
Model Theory ◽  
Open Problem ◽  
Category Theory ◽  
Computable Model ◽  
Computable Model Theory ◽  
Arbitrary Characteristic ◽  
Faithful Functor ◽  
New Construction ◽  
Image Position ◽  
Countable Structure

AbstractFried and Kollár constructed a fully faithful functor from the category of graphs to the category of fields. We give a new construction of such a functor and use it to resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure${\cal S}$, there exists a countable field${\cal F}$of arbitrary characteristic with the same essential computable-model-theoretic properties as${\cal S}$. Along the way, we develop a new “computable category theory”, and prove that our functor and its partially defined inverse (restricted to the categories of countable graphs and countable fields) are computable functors.

scholarly journals Algebraic Surfaces of General Type with Small c21 in Positive Characteristic

2008 ◽  
Vol 191 ◽  
pp. 111-134 ◽  
Author(s):  
Christian Liedtke
Keyword(s):  
Characteristic Zero ◽  
General Type ◽  
Positive Characteristic ◽  
Algebraic Surfaces ◽  
Surfaces Of General Type ◽  
Arbitrary Characteristic ◽  
Numerical Invariants ◽  
Characteristic 2

AbstractWe establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we show that Horikawa surfaces lift to characteristic zero.

scholarly journals Injective linear series of algebraic curves on quadrics

2020 ◽  
Vol 66 (2) ◽  
pp. 231-254
Author(s):  
Edoardo Ballico ◽  
Emanuele Ventura
Keyword(s):  
Algebraic Geometry ◽  
Projective Space ◽  
Algebraic Curves ◽  
Linear Series ◽  
Central Importance ◽  
Arbitrary Characteristic ◽  
Space Curves

Abstract We study linear series on curves inducing injective morphisms to projective space, using zero-dimensional schemes and cohomological vanishings. Albeit projections of curves and their singularities are of central importance in algebraic geometry, basic problems still remain unsolved. In this note, we study cuspidal projections of space curves lying on irreducible quadrics (in arbitrary characteristic).

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