A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory

Details A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory

1998-04-24

arxiv.org/abs/math/9804120v2

Ann. of Math. (2) 151 (2000), no. 3, 1025-1070

Mathematics

Algebraic Geometry

46 pages, published version

Scientific paper

Let $f: X \to S$ be flat morphism over an algebraically closed field $k$ with a relative normal crossings divisor $Y\subset X$, $(E, \nabla)$ be a bundle with a connection with log poles along $Y$ and curvature with values in $f^*\Omega^2_{k(S)}$. Then the Gau\ss-Manin sheaf $R^if_*(\Omega^*_{X/S}({\rm log} Y)\otimes E)$ carries a Gau\ss-Manin connection $GM^i(\nabla)$. We establish a Riemann-Roch formula relating the algebraic Chern-Simons invariants of $\nabla$, $GM^i(\nabla)$ and the top Chern class of $\Omega^1_{X/S}({\rm log}Y)$.

Affiliated with

Also associated with

No associations

Rating

A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-126197