scholarly journals The affine part of the Picard scheme

2009 ◽  
Vol 145 (2) ◽  
pp. 415-422 ◽  
Author(s):  
Thomas Geisser
Keyword(s):  
Maximal Torus ◽  
Perfect Field ◽  
Unipotent Subgroup ◽  
Picard Variety ◽  
Picard Scheme ◽  
Affine Part

AbstractWe describe the maximal torus and maximal unipotent subgroup of the Picard variety of a proper scheme over a perfect field.

scholarly journals Corrigendum: The affine part of the Picard scheme

2021 ◽  
Vol 157 (10) ◽  
pp. 2338-2340
Author(s):  
Thomas Geisser
Keyword(s):  
Corrected Version ◽  
Picard Scheme ◽  
Affine Part

Abstract We give a corrected version of Theorem 3, Lemma 4, and Proposition 9 in the above-mentioned paper, which are incorrect as stated (as was pointed out by O. Gabber).

scholarly journals A decomposition formula for representations

1987 ◽  
Vol 107 ◽  
pp. 63-68 ◽  
Author(s):  
George Kempf
Keyword(s):  
Irreducible Representation ◽  
General Formula ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Maximal Torus ◽  
Reductive Group ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Know How ◽  
Decomposition Formula

Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

scholarly journals Orthogonal groups containing a given maximal torus

2003 ◽  
Vol 266 (1) ◽  
pp. 87-101 ◽  
Author(s):  
Rosali Brusamarello ◽  
Pascale Chuard-Koulmann ◽  
Jorge Morales
Keyword(s):  
Maximal Torus ◽  
Orthogonal Groups

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.

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.

A broadband perfect field rotator

2011 ◽  
Vol 7 (3) ◽  
pp. 315-318 ◽  
Author(s):  
Qian-nan Wu ◽  
Ya-dong Xu ◽  
Huan-yang Chen
Keyword(s):  
Perfect Field

Perfect field concentrator using zero index metamaterials and perfect electric conductors

2013 ◽  
Vol 9 (1) ◽  
pp. 90-93 ◽  
Author(s):  
Mohammad Mehdi Sadeghi ◽  
Hamid Nadgaran ◽  
Huanyang Chen
Keyword(s):  
Perfect Field ◽  
Field Concentrator ◽  
Zero Index

Harish-Chandra Modules over ℤ

2019 ◽  
pp. 126-167
Author(s):  
Günter Harder
Keyword(s):  
Fixed Points ◽  
Lie Algebra ◽  
Lie Group ◽  
Maximal Torus ◽  
Reductive Group ◽  
Group Scheme ◽  
Finitely Generated ◽  
Cartan Involution ◽  
Split Maximal Torus ◽  
Definition Of

This chapter shows that certain classes of Harish-Chandra modules have in a natural way a structure over ℤ. The Lie group is replaced by a split reductive group scheme G/ℤ, its Lie algebra is denoted by 𝖌ℤ. On the group scheme G/ℤ there is a Cartan involution 𝚯 that acts by t ↦ t −1 on the split maximal torus. The fixed points of G/ℤ under 𝚯 is a flat group scheme 𝒦/ℤ. A Harish-Chandra module over ℤ is a ℤ-module 𝒱 that comes with an action of the Lie algebra 𝖌ℤ, an action of the group scheme 𝒦, and some compatibility conditions is required between these two actions. Finally, 𝒦-finiteness is also required, which is that 𝒱 is a union of finitely generated ℤ modules 𝒱I that are 𝒦-invariant. The definitions imitate the definition of a Harish-Chandra modules over ℝ or over ℂ.

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