000001812 001__ 1812
000001812 005__ 20250923113604.0
000001812 0247_ $$2doi$$a10.6082/uchicago.1812
000001812 037__ $$aTHESIS$$bDissertation
000001812 041__ $$aeng
000001812 245__ $$aIntersection Pairing of Cycles and Biextensions
000001812 260__ $$bUniversity of Chicago
000001812 269__ $$a2019-06
000001812 300__ $$a102
000001812 336__ $$aDissertation
000001812 502__ $$bPh.D.
000001812 520__ $$aWe 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.
000001812 540__ $$a© 2019 Yordanka Aleksandrova Kovacheva
000001812 650__ $$aMathematics
000001812 653__ $$abiextension
000001812 653__ $$acycles
000001812 653__ $$adeterminants
000001812 653__ $$aintersection
000001812 653__ $$aKnudsen-Mumford
000001812 653__ $$apairing
000001812 690__ $$aPhysical Sciences Division
000001812 691__ $$aMathematics
000001812 7001_ $$aKovacheva, Yordanka Aleksandrova$$uUniversity of Chicago
000001812 72012 $$aMadhav V. Nori
000001812 72014 $$aAlexander A. Beilinson
000001812 8564_ $$9dc2ef3d4-f049-494f-b0ff-7d09bf5b8001$$ePublic$$s492566$$uhttps://knowledge.uchicago.edu/record/1812/files/Kovacheva_uchicago_0330D_14734.pdf
000001812 909CO $$ooai:uchicago.tind.io:1812$$pDissertations$$pGLOBAL_SET
000001812 983__ $$aDissertation