On cubic torsors, biextensions and Severi–Brauer varieties over Abelian varieties
نویسندگان
چکیده
We study the homogeneous irreducible Severi-Brauer varieties over an Abelian variety $A$. Such objects were classified by Brion, \cite{Bri}. Here we interpret that result within context of cubical structures and biextensions for certain $\G_m$-torsors finite subgroups Our results can be seen as instance theory developed Breen, \cite{Breen:1983}, Moret-Bailly, \cite{Moret-Bailly}.
منابع مشابه
Semistable Abelian Varieties over Q
We prove that for N = 6 and N = 10, there do not exist any non-zero semistable abelian varieties over Q with good reduction outside primes dividingN . Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer–Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over Q with go...
متن کاملAbelian varieties over finite fields
A. Weil proved that the geometric Frobenius π = Fa of an abelian variety over a finite field with q = pa elements has absolute value √ q for every embedding. T. Honda and J. Tate showed that A 7→ πA gives a bijection between the set of isogeny classes of simple abelian varieties over Fq and the set of conjugacy classes of q-Weil numbers. Higher-dimensional varieties over finite fields, Summer s...
متن کاملHomogeneous bundles over abelian varieties
We obtain characterizations and structure results for homogeneous principal bundles over abelian varieties, that generalize work of Miyanishi and Mukai on homogeneous vector bundles. For this, we rely on notions and methods of algebraic transformation groups, especially observable subgroups and anti-affine groups.
متن کاملRegularity on abelian varieties
I will introduce the notion of Mukai regularity for coherent sheaves on abelian varieties, defined via conditions on the supports of the cohomologies of Fourier-Mukai transform complexes. In a very special form, depending on the choice of a polarization, this resembles and in fact strenghtens the classical notion of Castelnuovo-Mumford regularity. The techniques are in part a generalization of ...
متن کاملCubic threefolds and abelian varieties of dimension five. II
This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli space of principally polarized abelian varieties (ppavs) of dimension five, is an irreducible component of the locus of ppavs whose theta divisor has a point of multiplicity three or more. This paper also gives a sharp bound on the multiplicity...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The São Paulo Journal of Mathematical Sciences
سال: 2021
ISSN: ['2316-9028', '1982-6907']
DOI: https://doi.org/10.1007/s40863-021-00250-3