scholarly journals Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes

2005 ◽  
Vol 54 (1) ◽  
pp. 263-308 ◽  
Author(s):  
Paul Bressler ◽  
Valery A. Lunts
Keyword(s):  
Intersection Cohomology ◽  
Lefschetz Theorem ◽  
Hard Lefschetz Theorem

scholarly journals Hard Lefschetz theorem for Vaisman manifolds

2018 ◽  
Vol 371 (2) ◽  
pp. 755-776
Author(s):  
Beniamino Cappelletti-Montano ◽  
Antonio De Nicola ◽  
Juan Carlos Marrero ◽  
Ivan Yudin
Keyword(s):  
Lefschetz Theorem ◽  
Vaisman Manifolds ◽  
Hard Lefschetz Theorem

Proof of the Hard Lefschetz Theorem

2020 ◽  
pp. 401-418
Author(s):  
Ben Elias ◽  
Shotaro Makisumi ◽  
Ulrich Thiel ◽  
Geordie Williamson
Keyword(s):  
Lefschetz Theorem ◽  
Hard Lefschetz Theorem

scholarly journals Examples of compact K-contact manifolds with no Sasakian metric

2014 ◽  
Vol 11 (09) ◽  
pp. 1460028 ◽  
Author(s):  
Beniamino Cappelletti-Montano ◽  
Antonio De Nicola ◽  
Juan Carlos Marrero ◽  
Ivan Yudin
Keyword(s):  
Sasakian Manifolds ◽  
Contact Manifolds ◽  
Lefschetz Theorem ◽  
Sasakian Metric ◽  
Hard Lefschetz Theorem

Using the hard Lefschetz theorem for Sasakian manifolds, we find two examples of compact K-contact nilmanifolds with no compatible Sasakian metric in dimensions 5 and 7, respectively.

scholarly journals Étale cohomology of rank one $$\ell $$-adic local systems in positive characteristic

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Hélène Esnault ◽  
Moritz Kerz
Keyword(s):  
Positive Characteristic ◽  
Vanishing Theorem ◽  
Deformation Spaces ◽  
Local Systems ◽  
Etale Cohomology ◽  
Lefschetz Theorem ◽  
Rank One ◽  
Étale Cohomology ◽  
Generic Vanishing ◽  
Hard Lefschetz Theorem

AbstractWe show that in positive characteristic special loci of deformation spaces of rank one $$\ell $$ ℓ -adic local systems are quasi-linear. From this we deduce the Hard Lefschetz theorem for rank one $$\ell $$ ℓ -adic local systems and a generic vanishing theorem.

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