Resolution of singularities and modular Galois theory

By Shreeram S. Abhyankar. 2000

54 citations recorded by the source corpus.

I shall sketch a brief history of the desingularization problem from Riemann thru Zariski to Hironaka, including the part I played in it and the work on Galois theory which this led me to, and how that caused me to search out many group theory gurus. I shall also formulate several conjectures and suggest numerous thesis problems.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0b1d05c1cdf9bd8c16b0616ccc2f20066b7e2a5c

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Resolution of singularities of threefolds in positive characteristic. I.: Reduction to local uniformization on Artin–Schreier and purely inseparable coverings (2008, unknown): “See [6] for a survey and open problems related to simultaneous resolution along a valuation.”
RESOLUTION OF SINGULARITIES OF THREEFOLDS IN POSITIVE CHARACTERISTIC II (2008, background): “See [ 6 ] for a survey and open problems related to simultaneous resolution along a valuation.”
Ramification of valuations (2004, unknown): “RAMIFICATION OF VALUATIONS STEVEN DALE CUTKOSKY AND OLIVIER PILTANT”
Singular Points of Plane Curves (2004, background): “For if A : F × [0, 1] → F × [0, 1] is a level preserving map with A(x, 0) = h(x) and A(x, 1) = h′(x) for each x ∈ F , A induces a diffeomorphism between the two quotient spaces.”
Resolution of Singularities (2004, background): “This was conjectured by Abhyankar on page 144 [8] (and is implicit in [1]).”