scholarly journals On the derived category of Grassmannians in arbitrary characteristic

2015 ◽  
Vol 151 (7) ◽  
pp. 1242-1264 ◽  
Author(s):  
Ragnar-Olaf Buchweitz ◽  
Graham J. Leuschke ◽  
Michel Van den Bergh
Keyword(s):  
Endomorphism Ring ◽  
Characteristic Zero ◽  
Derived Category ◽  
Simple Modules ◽  
Arbitrary Characteristic ◽  
Tilting Bundle

In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov’s well-known characteristic-zero results, we construct dual exceptional collections on them (which are, however, not strong) as well as a tilting bundle. We show that this tilting bundle has a quasi-hereditary endomorphism ring and we identify the standard, costandard, projective and simple modules of the latter.

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.

One-Sided Inverses in Rings

1975 ◽  
Vol 27 (1) ◽  
pp. 218-224 ◽  
Author(s):  
Roger D. Peterson
Keyword(s):  
Characteristic Zero ◽  
Commutative Rings ◽  
Group Algebras ◽  
Group Rings ◽  
Matrix Rings ◽  
Von Neumann ◽  
Full Matrix ◽  
Arbitrary Characteristic

Following Herstein [2], we will call a ring R with identity von Neumann finite (vNf) provided that xy = 1 implies yx — WnR. Kaplansky [4] showed that group algebras over fields of characteristic zero are vNf rings, and further, that full matrix rings over such rings are also vNf. Herstein [2] has posed the problem for group algebras over fields of arbitrary characteristic. If group algebras over fields are always vNf, then it is easily seen that group algebras over commutative rings are always vNf. What conditions on the underlying ring of scalars would force the vNf property for all group rings over it?

scholarly journals Tilting Bundles on Hypertoric Varieties

2019 ◽  
Author(s):  
Špela Špenko ◽  
Michel Van den Bergh
Keyword(s):  
Linear Space ◽  
Endomorphism Ring ◽  
Invariant Theory ◽  
Short Note ◽  
Regular Sequence ◽  
Geometric Invariant Theory ◽  
Geometric Invariant ◽  
Finite Characteristic ◽  
Tilting Bundle ◽  
Hypertoric Varieties

Abstract Recently McBreen and Webster constructed a tilting bundle on a smooth hypertoric variety (using reduction to finite characteristic) and showed that its endomorphism ring is Koszul. In this short note we present alternative proofs for these results. We simply observe that the tilting bundle constructed by Halpern-Leistner and Sam on a generic open Geometric Invariant Theory substack of the ambient linear space restricts to a tilting bundle on the hypertoric variety. The fact that the hypertoric variety is defined by a quadratic regular sequence then also yields an easy proof of Koszulity.

scholarly journals Formal orbifolds and orbifold bundles in positive characteristic

2019 ◽  
Vol 30 (12) ◽  
pp. 1950067
Author(s):  
Manish Kumar ◽  
A. J. Parameswaran
Keyword(s):  
Fundamental Group ◽  
Characteristic Zero ◽  
Vector Bundles ◽  
Positive Characteristic ◽  
Closed Field ◽  
Fundamental Groups ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Algebraically Closed Field ◽  
Arbitrary Characteristic

We define formal orbifolds over an algebraically closed field of arbitrary characteristic as curves together with some branch data. Their étale coverings and their fundamental groups are also defined. These fundamental groups approximate the fundamental group of an appropriate affine curve. We also define vector bundles on these objects and the category of orbifold bundles on any smooth projective curve. Analogues of various statements about vector bundles which are true in characteristic zero are also proved. Some of these are positive characteristic avatars of notions which appear in the second author’s work [A. J. Parmeswaran, Parabolic coverings I: Case of curves, J. Ramanujam Math. Soc. 25(3) (2010) 233–251.] in characteristic zero.

scholarly journals Actions of the additive group Ga on certain noncommutative deformations of the plane

2021 ◽  
Vol 29 (2) ◽  
pp. 269-279
Author(s):  
Ivan Kaygorodov ◽  
Samuel A. Lopes ◽  
Farukh Mashurov
Keyword(s):  
Automorphism Group ◽  
Polynomial Ring ◽  
Characteristic Zero ◽  
Weyl Algebra ◽  
Additive Group ◽  
Prime Characteristic ◽  
Arbitrary Characteristic ◽  
Arbitrary Polynomial ◽  
Comodule Algebra ◽  
The Family

Abstract We connect the theorems of Rentschler [18] and Dixmier [10] on locally nilpotent derivations and automorphisms of the polynomial ring A 0 and of the Weyl algebra A 1, both over a field of characteristic zero, by establishing the same type of results for the family of algebras A h = 〈 x , y | y x − x y = h ( x ) 〉 , {A_h} = \left\langle {x,y|yx - xy = h\left( x \right)} \right\rangle , , where h is an arbitrary polynomial in x. In the second part of the paper we consider a field 𝔽 of prime characteristic and study 𝔽[t]-comodule algebra structures on Ah . We also compute the Makar-Limanov invariant of absolute constants of Ah over a field of arbitrary characteristic and show how this subalgebra determines the automorphism group of Ah .

scholarly journals VI-modules in non-describing characteristic, part II

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Rohit Nagpal
Keyword(s):  
Characteristic Zero ◽  
Complete Classification ◽  
Arbitrary Characteristic ◽  
Characteristic Part

Abstract We classify all irreducible generic VI {\mathrm{VI}} -modules in non-describing characteristic. Our result degenerates to yield a classification of irreducible generic FI {\mathrm{FI}} -modules in arbitrary characteristic. Equivalently, we provide a complete classification of irreducibles of admissible 𝐆𝐋 ∞ ⁢ ( 𝔽 q ) {\mathbf{GL}_{\infty}(\mathbb{F}_{q})} -representations in non-describing characteristic, which is new even in characteristic zero. This result degenerates to provide a complete classification of irreducibles of admissible S ∞ {S_{\infty}} -representations in arbitrary characteristic, which is new away from characteristic zero.

scholarly journals Equimultiple Locus of Embedded Algebroid Surfaces and Blowing-up in Arbitrary Characteristic

2009 ◽  
Vol 16 (04) ◽  
pp. 575-586
Author(s):  
R. Piedra ◽  
J. M. Tornero
Keyword(s):  
Characteristic Zero ◽  
Ground Field ◽  
Arbitrary Characteristic ◽  
Blowing Up

This paper describes the behaviour of the equimultiple locus of algebroid surfaces under blowing-up for an arbitrary characteristic ground field, extending previous results of the authors for characteristic zero.

Solvable Points on Projective Algebraic Curves

2004 ◽  
Vol 56 (3) ◽  
pp. 612-637 ◽  
Author(s):  
Ambrus Pál
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Algebraic Curves ◽  
Residue Field ◽  
Rational Points ◽  
Projective Curve ◽  
Arbitrary Characteristic ◽  
Projective Curves ◽  
Solvable Extension ◽  
Solvable Points

AbstractWe examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g, when g is at least 40, over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 defined over any field has a solvable point. Finally we prove that every genus 1 curve defined over a local field of characteristic zero with residue field of characteristic p has a divisor of degree prime to 6p defined over a solvable extension.

scholarly journals DESCRIPTION OF SIMPLE MODULES FOR SCHUR SUPERALGEBRA S(2|2)

2013 ◽  
Vol 55 (3) ◽  
pp. 695-719 ◽  
Author(s):  
A. N. GRISHKOV ◽  
F. MARKO
Keyword(s):  
Characteristic Zero ◽  
Positive Characteristic ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Simple Modules ◽  
Schur Superalgebra

AbstractThe goal of this paper is to describe explicitly simple modules for Schur superalgebra S(2|2) over an algebraically closed field K of characteristic zero or positive characteristic p>2.

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