scholarly journals An elementary, explicit, proof of the existence of Quot schemes of points

2007 ◽  
Vol 231 (2) ◽  
pp. 401-415 ◽  
Author(s):  
Trond Gustavsen ◽  
Dan Laksov ◽  
Roy Skjelnes
Keyword(s):  
Quot Schemes ◽  
Explicit Proof

Stability of sheaves over Quot schemes

2018 ◽  
Vol 149 ◽  
pp. 66-85 ◽  
Author(s):  
Chandranandan Gangopadhyay
Keyword(s):  
Quot Schemes

scholarly journals General Hilbert stacks and Quot schemes

2015 ◽  
Vol 64 (2) ◽  
pp. 335-347 ◽  
Author(s):  
Jack Hall ◽  
David Rydh
Keyword(s):  
Quot Schemes

scholarly journals ON THE VOEVODSKY MOTIVE OF THE MODULI STACK OF VECTOR BUNDLES ON A CURVE

2020 ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Vector Bundles ◽  
Intersection Theory ◽  
Line Bundles ◽  
Projective Curve ◽  
Classifying Space ◽  
Smooth Projective Curve ◽  
Quot Schemes ◽  
Homotopy Colimit ◽  
Moduli Stack ◽  
Fixed Rank

Abstract We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky’s category of motives. We prove that this motive can be written as a homotopy colimit of motives of smooth projective Quot schemes of torsion quotients of sums of line bundles on the curve. When working with rational coefficients, we prove that the motive of the stack of bundles lies in the localizing tensor subcategory generated by the motive of the curve, using Białynicki-Birula decompositions of these Quot schemes. We conjecture a formula for the motive of this stack, inspired by the work of Atiyah and Bott on the topology of the classifying space of the gauge group, and we prove this conjecture modulo a conjecture on the intersection theory of the Quot schemes.

scholarly journals THE NON-ABELIAN TENSOR PRODUCT OF FINITE GROUPS IS FINITE: A HOMOLOGY-FREE PROOF

2010 ◽  
Vol 52 (3) ◽  
pp. 473-477 ◽  
Author(s):  
VIJI Z. THOMAS
Keyword(s):  
Tensor Product ◽  
Finite Groups ◽  
Explicit Proof

AbstractIn this note, we give a homology-free proof that the non-abelian tensor product of two finite groups is finite. In addition, we provide an explicit proof that the non-abelian tensor product of two finite p-groups is a finite p-group.

Why is It?

1926 ◽  
Vol 19 (3) ◽  
pp. 169-173
Author(s):  
P. Stroup
Keyword(s):  
High School ◽  
The Other ◽  
Explicit Proof

I have just looked through copies of 10 current high school geometries and in not one of them can I find a direct and explicit proof of the fact that if the square on one side of a triangle equals the sum of the squares on the other 2 sides, it is a right triangle. In some books it is proved indirectly by proving its converse and its opposite, but no attention is called to the fact. Some authors use the fact in problems without having proved it or mentioned it and these same authors seem worried in their opening chapters if the converse of any little proposition is assumed to be true without giving the proof of it.

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