CLASS INVARIANTS FOR ABELIAN VARIETIES OF HIGHER DIMENSION

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The principal subject of this research project is geometric Galois structure . Galois structure appeared first in number theory, and has motivated research of many people. This subject was later extended in the context of arithmetic algebraic geometry. More precisely, Martin Taylor has stated in 1988 a conjecture which says that certain Galois structure invariants attached to elliptic curves, should vanish. This has been established by Taylor and others. Now, my aim is to obtain positive results on (an analogue of) Taylor's conjecture for abelian varieties of higher dimension.Taylor's conjecture is stated in the context of varieties having everywhere good reduction. A natural question to ask is : what does happens in the bad reduction case ? In my PhD, I have shown how Taylor's conjecture can be generalized to semi-stable abelian varieties. Also, I have proven that the vanishing result was still true, in some extent, for semi-stable elliptic curves. As the semi-stable case is much more frequent than the good reduction case, this enlarges the field of investigations. In this context, counter-examples to Taylor's conjecture can be expected to be found.This project can establish collaboration with researchers abroad (from countries like Germany, France and the US).AMS MSC code : 11Gxx, 11Rxx, 14Kxx