@article{Intersection:1812,
      recid = {1812},
      author = {Kovacheva, Yordanka Aleksandrova},
      title = {Intersection Pairing of Cycles and Biextensions},
      publisher = {The University of Chicago},
      school = {Ph.D.},
      address = {2019-06},
      pages = {102},
      abstract = {We consider an intersection pairing of cycles, as well as  the corresponding biextension. More specifically, we  construct a pairing $L: Z^p(X)\times Z^q(X)\to Z^1(S)$   between all codimensions $p$ and $q$ cycles on a variety  $X$ of relative dimension $d$ over a base $S$, both over a  field $F$. The main question we consider is under what  conditions on the codimension $q$ cycle $D$ on $X$, all  rational equivalences between two codimension $p$ cycles  $A$ and $A'$ on $X$ become the same rational equivalence  between the divisors $L(A, D)$ and $L(A', D)$ on $S$. For  cycles $D$ that are algebraically trivial on the generic  fiber $X_{\eta}$, the divisors on $S$ do not depend on the  rational equivalence of the codimension $p$ cycles.  Nevertheless, for numerically trivial divisors and zero  cycles, the image does depend on the rational equivalence  of the zero cycles. Therefore, Bloch's biextension of  $\CH^p_{hom}(X)\times \CH_{hom}^q(X)$ by $F^{\times}$ can  not be extended to the numerically trivial cycles. As a  part of the proof of the numerically trivial case, we give  an explicit expression of the Suslin-Voevodsky  isomorphism.},
      url = {http://knowledge.uchicago.edu/record/1812},
      doi = {https://doi.org/10.6082/uchicago.1812},
}