Explicit Deligne pairing release_r622ydofyfgqfbbbyuvgysftlu

Abstract

<jats:title>Abstract</jats:title>We give an explicit formula for the Deligne pairing for proper and flat morphisms <jats:inline-formula><jats:alternatives><jats:tex-math>$$f:X\rightarrow S$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo>→</mml:mo> <mml:mi>S</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> of schemes, in terms of the determinant of cohomology. The whole construction is justified by an analogy with the intersection theory on non-singular projective algebraic varieties.
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