Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative cycles with moduli and regulator maps   Let X be a separated scheme of finite type over a field k and D a non-reduced
effective Cartier divisor on it. We attach to the pair (X, D) a cycle complex
with modulus, whose homotopy groups - called higher Chow groups with modulus -
generalize additive higher Chow groups of Bloch-Esnault, R\"ulling, Park and
Krishna-Levine, and that sheafified on $X_{Zar}$ gives a candidate definition
for a relative motivic complex of the pair, that we compute in weight 1.
  When X is smooth over k and D is such that $D_{red}$ is a normal crossing
divisor, we construct a fundamental class in the cohomology of relative
differentials for a cycle satisfying the modulus condition, refining El-Zein's
explicit construction. This is used to define a natural regulator map from the
relative motivic complex of (X,D) to the relative de Rham complex. When X is
defined over $\mathbb{C}$, the same method leads to the construction of a
regulator map to a relative version of Deligne cohomology, generalizing Bloch's
regulator from higher Chow groups.
  Finally, when X is moreover connected and proper over $\mathbb{C}$, we use
relative Deligne cohomology to define relative intermediate Jacobians with
modulus $J^r_{X|D}$ of the pair (X,D). For r= dim X, we show that $J^r_{X|D}$
is the universal regular quotient of the Chow group of 0-cycles with modulus.

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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: comp-gas