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Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves

Cristian González-Avilés — 2009

Open Mathematics

We obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves over perfect fields. For example, if k is finitely generated over ℚ and X → C is a quadric fibration of odd relative dimension at least 11, then CH i(X) is finitely generated for i ≤ 4.

Flasque resolutions of reductive group schemes

Cristian González-Avilés — 2013

Open Mathematics

We generalize Colliot-Thélène’s construction of flasque resolutions of reductive group schemes over a field to a broad class of base schemes.

The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme

Mikhail Borovoi; Cristian González-Avilés — 2014

Open Mathematics

We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G↦ π1(G) is exact.

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