Eğrilerin bir çarpımı üzerinde indirgenemez döngüler

In his pioneering work \cite{Blo1}, S.Bloch introduced higher Chow groups, denoted by $CH^n(X,m)$ as a natural generalization of the classical case and generalized the Grothendieck amended Riemann Roch theorem to these groups, which states that the higher Chow ring and higher $K$-theory of a projective algebraic manifold are isomorphic working over rationals. This brilliant invention of Bloch brought a new insight to the study of algebraic cycles and $K$-theory. In this thesis, we study ``interesting cycle classes" , namely indecomposable cycles for products of curves. In the case $m=1$, indecomposable cycles are cycles in $CH^n(X,1)$ which do not come from the image of the intersection pairing $CH^1(X,1) \otimes CH^{n-1}(X)$. We prove that the group of indecomposable cycles, $CH_{ind}^2(X,1; \Qq)$, is nontrivial for a sufficiently general product of two elliptic curves.