arXiv subjects

Parker Lowrey

Publications and source records attributed to Parker Lowrey.

2 recordsLinked to original sources

arXiv2014

Derived algebraic cobordism

We construct a cohomology theory using quasi-smooth derived schemes as generators and an analogue of the bordism relation using derived fibre products as relations. This theory has pull-backs along all morphisms between smooth schemes independent of any characteristic assumptions. We prove that in characteristic zero, the resulting theory agrees with algebraic cobordism as defined by Levine and Morel. We thus obtain a new set of generators and relations for algebraic cobordism.

math.AG↗

arXiv2012

Grothendieck-Riemann-Roch for derived schemes

We define bivariant algebraic K-theory and bivariant derived Chow on the homotopy category of derived schemes over a smooth base. The orientation on the latter corresponds to virtual Gysin homomorphisms. We then provide a morphism between these two bivariant theories and compare the two orientations. This comparison then yields a homological and cohomological Grothendieck-Riemann-Roch formula for virtual classes.

math.AG↗