Tate module tensor decompositions and the Sato–Tate conjecture for certain abelian varieties potentially of $$\mathrm {GL}_2$$-type
نویسندگان
چکیده
We introduce a tensor decomposition of the $$\ell $$ -adic Tate module an abelian variety $$A_0$$ defined over number field which is geometrically isotypic. If potentially $$\mathrm {GL}_2$$ -type and totally real field, we use this to describe its Sato–Tate group prove conjecture in certain cases.
منابع مشابه
The Tate Conjecture for Certain Abelian Varieties over Finite Fields
In an earlier work, we showed that if the Hodge conjecture holds for all complex abelian varieties of CM-type, then the Tate conjecture holds for all abelian varieties over finite fields (Milne 1999b). In this article, we extract from the proof a statement (Theorem 1.1) that sometimes allows one to deduce the Tate conjecture for the powers of a single abelian variety A over a finite field from ...
متن کاملOn the Mumford–tate Conjecture for Abelian Varieties with Reduction Conditions
We study monodromy action on abelian varieties satisfying certain bad reduction conditions. These conditions allow us to get some control over the Galois image. As a consequence we verify the Mumford–Tate conjecture for such abelian varieties.
متن کاملthe investigation of the relationship between type a and type b personalities and quality of translation
چکیده ندارد.
The Breuil–mézard Conjecture for Potentially Barsotti–tate Representations
We prove the Breuil–Mézard conjecture for 2-dimensional potentially Barsotti–Tate representations of the absolute Galois group GK , K a finite extension of Qp, for any p > 2 (up to the question of determining precise values for the multiplicities that occur). In the case that K/Qp is unramified, we also determine most of the multiplicities. We then apply these results to the weight part of Serr...
متن کاملThe Tate pairing for Abelian varieties over finite fields
In this expository note, we describe an arithmetic pairing associated to an isogeny between Abelian varieties over a finite field. We show that it generalises the Frey–Rück pairing, thereby giving a short proof of the perfectness of the latter.
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: Mathematische Zeitschrift
سال: 2021
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-021-02895-4