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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,341 papers · 148 categories

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4 results for “Grothendieck-Lefschetz”

Twisted cohomology of configuration spaces and spaces of maximal tori via point-countingmath.GT

New recurrence formula for stable twisted Betti numbers of configuration spaces and spaces of maximal tori.

problem Computing stable twisted Betti numbers of configuration spaces and spaces of maximal tori.

method Computing twisted point-counts on algebraic varieties and using Grothendieck-Lefschetz fixed point formula.

result Stable twisted Betti numbers are linearly recurrent in i.

configuration spaces maximal tori twisted cohomology point-counting Grothendieck-Lefschetz

2016-03-12abs ↗pdf ↗

\mathrm{FI}_G

-modules and arithmetic statisticsmath.AG

Extends methods to study polynomial roots over finite fields.

problem Stability of arithmetic statistics for polynomial roots.

method FI_G-modules, Grothendieck-Lefschetz trace formula, subexponential bounds.

result Average value of Gauss sums stabilizes as polynomial degree increases.

FI_G-modules Galois representations orbit configuration spaces arithmetic statistics Gauss sums

2017-03-21abs ↗pdf ↗

Representation stability and arithmetic statistics of spaces of 0-cyclesmath.AT

Study stabilizes arithmetic statistics of rational maps over finite fields.

problem Stability of arithmetic statistics of rational maps over finite fields.

method Representation stability and arithmetic statistics of spaces of 0-cycles.

result Arithmetic quantities associated to rational maps over finite fields stabilize as degree increases.

representation stability arithmetic statistics rational maps finite fields cohomology

2017-10-18abs ↗pdf ↗

Representation stability in cohomology and asymptotics for families of varieties over finite fieldsmath.GT

We consider two families X_n of varieties on which the symmetric group S_n acts: the configuration space of n points in C and the space of n linearly independent lines in C^n. Given an irreducible S_n-representation V, one can ask how the multiplicity of V in the cohomology groups H*(X_n;Q) varies with n. We explain ho…

2013-09-24abs ↗pdf ↗