On Some Arithmetic Problems Related to the Hodge Cycles on the Fermat Varieties.
On Some Arithmetic Problems Related to the Hodge Cycles on the Fermat Varieties (Erratum).
On Tate’s refinement for a conjecture of Gross and its generalization
We study Tate’s refinement for a conjecture of Gross on the values of abelian -function at and formulate its generalization to arbitrary cyclic extensions. We prove that our generalized conjecture is true in the case of number fields. This in particular implies that Tate’s refinement is true for any number field.
On the Tate-Shafarevich group of semistable elliptic curves with a rational 3-torsion
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