scholarly journals On Elements of Prime Order in the Plane Cremona Group over a Perfect Field

2009 ◽  
Author(s):  
I. V. Dolgachev ◽  
V. A. Iskovskikh
Keyword(s):  
Prime Order ◽  
Perfect Field ◽  
Cremona Group

Algebraic subgroups of the plane Cremona group over a perfect field

2021 ◽  
Vol Volume 5 ◽  
Author(s):  
Julia Schneider ◽  
Susanna Zimmermann
Keyword(s):  
Rational Points ◽  
Perfect Field ◽  
Algebraic Subgroup ◽  
Cremona Group ◽  
Birational Map

We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in a maximal algebraic subgroup of the plane Cremona group. We classify the maximal groups, and their subgroups of rational points, up to conjugacy by a birational map.

Bound for the order for p-elementary subgroups in the plane cremona group over a perfect field

2012 ◽  
Vol 56 (2) ◽  
pp. 509-513
Author(s):  
A. L. Fomin
Keyword(s):  
Sharp Bound ◽  
Perfect Field ◽  
Cremona Group

AbstractWe obtain a sharp bound for p-elementary subgroups in the Cremona group Cr2(k) over an arbitrary perfect field k.

RELATIONS IN THE TWO-DIMENSIONAL CREMONA GROUP OVER A PERFECT FIELD

1994 ◽  
Vol 42 (3) ◽  
pp. 427-478 ◽  
Author(s):  
V A Iskovskikh ◽  
F K Kabdykairov ◽  
S L Tregub
Keyword(s):  
Two Dimensional ◽  
Perfect Field ◽  
Cremona Group

scholarly journals On stable conjugacy of finite subgroups of the plane Cremona group, I

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Fedor Bogomolov ◽  
Yuri Prokhorov
Keyword(s):  
Prime Order ◽  
Cremona Group ◽  
Cyclic Groups ◽  
Group I ◽  
Finite Subgroups ◽  
Birational Invariant

AbstractWe discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We compute the stable birational invariant H 1(G, Pic(X)) for cyclic groups of prime order.

Functional encryption for computational hiding in prime order groups via pair encodings

2017 ◽  
Vol 86 (1) ◽  
pp. 97-120 ◽  
Author(s):  
Jongkil Kim ◽  
Willy Susilo ◽  
Fuchun Guo ◽  
Man Ho Au
Keyword(s):  
Prime Order ◽  
Functional Encryption

scholarly journals Ordinary varieties with trivial canonical bundle are not uniruled

2021 ◽  
Author(s):  
Zsolt Patakfalvi ◽  
Maciej Zdanowicz
Keyword(s):  
Canonical Bundle ◽  
Perfect Field ◽  
Tangent Bundles

AbstractWe prove that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic $$p>0$$ p > 0 are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our work, together with Langer’s results, implies that varieties of the above type have strongly semistable tangent bundles with respect to every polarization.

scholarly journals p-Elementary subgroups of the Cremona group

2007 ◽  
Vol 314 (2) ◽  
pp. 553-564 ◽  
Author(s):  
Arnaud Beauville
Keyword(s):  
Cremona Group

A Note on Geometric Factoriality

1995 ◽  
Vol 38 (4) ◽  
pp. 390-395 ◽  
Author(s):  
S. M. Bhatwadekar ◽  
K. P. Russell
Keyword(s):  
Finite Groups ◽  
Positive Answer ◽  
Integral Representations ◽  
Perfect Field ◽  
Polynomial Algebras ◽  
Representations Of Finite Groups ◽  
Smooth Affine

AbstractLet k: be a perfect field such that is solvable over k. We show that a smooth, affine, factorial surface birationally dominated by affine 2-space is geometrically factorial and hence isomorphic to . The result is useful in the study of subalgebras of polynomial algebras. The condition of solvability would be unnecessary if a question we pose on integral representations of finite groups has a positive answer.

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