Periods and Algebraic deRham Cohomology

Authors: 
Friedrich, Benjamin
Year: 
2004
Language: 
English
Abstract: 
{Abstract} It is known that the algebraic deRham cohomology group $h_{DR}{i}(X_0/$ of a nonsingular variety $X_0/ has the same rank as the rational singular cohomology group $h^i$ of the complex manifold $ associated to the base change $X_0{amp;#125;. However, we do not have a natural isomorphism $amp;#123;i}(X_0/isoh^i$. Any choice of such an isomorphism produces certain integrals, so called periods, which reveal valuable information about $X_0$. The aim of this thesis is to explain these classical facts in detail. Based on an approach of Kontsevich te[pp.~62--64]{kontsevich}, different definitions of a period are compared and their properties discussed. Finally, the theory is applied to some examples. These examples include a representation of $2)$ as a period and a variation of mixed Hodge structures used by Goncharov te{goncharov}.
Pubdate / Erscheinungsdatum: 
2004.03.23
Promoter / Gefördert durch: 
Studienstiftung des deutschen Volkes
Pages / Seitenanzahl: 
101
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