scholarly journals Fourier transforms, generic vanishing theorems and polarizations of abelian varieties

2000 ◽  
Vol 235 (4) ◽  
pp. 717-726 ◽  
Author(s):  
Christopher D. Hacon
Keyword(s):  
Fourier Transforms ◽  
Abelian Varieties ◽  
Vanishing Theorems ◽  
Generic Vanishing

scholarly journals Topology of Subvarieties of Complex Semi-abelian Varieties

2020 ◽  
Author(s):  
Yongqiang Liu ◽  
Laurentiu Maxim ◽  
Botong Wang
Keyword(s):  
Euler Characteristic ◽  
Morse Theory ◽  
Characteristic Property ◽  
Abelian Varieties ◽  
Betti Numbers ◽  
Local Systems ◽  
Affine Manifolds ◽  
Cyclic Covers ◽  
Rank One ◽  
Generic Vanishing

Abstract We use the non-proper Morse theory of Palais–Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties and that of their infinite cyclic covers. As main applications, we obtain the finite generation (except in the middle degree) of the corresponding integral Alexander modules as well as the signed Euler characteristic property and generic vanishing for rank-one local systems on such subvarieties. Furthermore, we give a more conceptual (topological) interpretation of the signed Euler characteristic property in terms of vanishing of Novikov homology. As a byproduct, we prove a generic vanishing result for the $L^2$-Betti numbers of very affine manifolds. Our methods also recast June Huh’s extension of Varchenko’s conjecture to very affine manifolds and provide a generalization of this result in the context of smooth closed sub-varieties of semi-abelian varieties.

scholarly journals Vanishing theorems for perverse sheaves on abelian varieties, revisited

2017 ◽  
Vol 24 (1) ◽  
pp. 63-84 ◽  
Author(s):  
Bhargav Bhatt ◽  
Christian Schnell ◽  
Peter Scholze
Keyword(s):  
Abelian Varieties ◽  
Vanishing Theorems ◽  
Perverse Sheaves

scholarly journals Generic vanishing in characteristic p > 0 and the characterization of ordinary abelian varieties

2016 ◽  
Vol 138 (4) ◽  
pp. 963-998 ◽  
Author(s):  
Christopher D. Hacon ◽  
Zsolt Patakfalvi
Keyword(s):  
Abelian Varieties ◽  
Characteristic P ◽  
Generic Vanishing

scholarly journals GENERIC VANISHING THEORY VIA MIXED HODGE MODULES

2013 ◽  
Vol 1 ◽  
Author(s):  
MIHNEA POPA ◽  
CHRISTIAN SCHNELL
Keyword(s):  
Abelian Varieties ◽  
Local Systems ◽  
Coherent Sheaves ◽  
Natural Categories ◽  
Rank One ◽  
Generic Vanishing ◽  
Mixed Hodge Modules ◽  
Irregular Varieties

AbstractWe extend most of the results of generic vanishing theory to bundles of holomorphic forms and rank-one local systems, and more generally to certain coherent sheaves of Hodge-theoretic origin associated with irregular varieties. Our main tools are Saito’s mixed Hodge modules, the Fourier–Mukai transform for $\mathscr{D}$-modules on abelian varieties introduced by Laumon and Rothstein, and Simpson’s harmonic theory for flat bundles. In the process, we also discover two natural categories of perverse coherent sheaves.

scholarly journals Generic vanishing and minimal cohomology classes on abelian varieties

2007 ◽  
Vol 340 (1) ◽  
pp. 209-222 ◽  
Author(s):  
Giuseppe Pareschi ◽  
Mihnea Popa
Keyword(s):  
Abelian Varieties ◽  
Generic Vanishing

Generic vanishing theorems [26], [14]

1992 ◽  
pp. 137-146
Author(s):  
Hélène Esnault ◽  
Eckart Viehweg
Keyword(s):  
Vanishing Theorems ◽  
Generic Vanishing

scholarly journals Vanishing theorems for constructible sheaves on abelian varieties

2015 ◽  
Vol 24 (3) ◽  
pp. 531-568 ◽  
Author(s):  
Thomas Krämer ◽  
Rainer Weissauer
Keyword(s):  
Abelian Varieties ◽  
Vanishing Theorems ◽  
Constructible Sheaves

scholarly journals Generic vanishing for semi-abelian varieties and integral Alexander modules

2018 ◽  
Vol 293 (1-2) ◽  
pp. 629-645 ◽  
Author(s):  
Yongqiang Liu ◽  
Laurentiu Maxim ◽  
Botong Wang
Keyword(s):  
Abelian Varieties ◽  
Generic Vanishing
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