• V Srinivas

Articles written in Proceedings – Mathematical Sciences

• Decomposition of the de Rham complex

We give a reformulation of Deligne and Illusie's characteristicp proof of the degeneration of the “Hodge-to-de Rham” spectral sequence, which replaces patching in the derived category by an explicit quasi-isomorphism.

• Gysin maps and cycle classes for Hodge cohomology

Iff:X→Y is a projective morphism between regular varieties over a field, we construct Gysin maps$$f_ * :H^i \left( {X,\Omega _{X/Z}^j } \right) \to H_{f(x)}^{i + d} \left( {X,\Omega _{Y/Z}^j } \right)$$ for the Hodge cohomology groups, whered-dimY-dimX. These Gysin maps have the expected properties, and in particular may be used to construct a cycle class map$$Cl_X :CH^i \left( {X,S} \right) \to H^i \left( {X,\Omega _{X/Z}^i } \right)$$ whereX is quasi-projective over a field,S is the singular locus, andCHi(X, S) is the relative Chow group of codimension-i cycles modulo rational equivalence. Simple properties of this cycle map easily imply the infinite dimensionality theorem for the Chow group of zero cycles of a normal projective varietyX overC with$$H^n \left( {X,\mathcal{O}_X } \right) \ne 0$$, wheren=dimX. One also recovers examples of Nori of affinen-dimensional varieties which support indecomposable vector bundles of rankn.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019