23 citations · 29 across the 5 of their papers we have counts for
6 papers
Eisenstein cohomology classes for over imaginary quadratic fields
Nicolas Bergeron, Pierre Charollois, Luis E. Garcia
We study the arithmetic of degree Eisenstein cohomology classes for locally symmetric spaces associated to over an imaginary quadratic field . Under natura…
Counting abelian varieties over finite fields via Frobenius densities
Jeff Achter, Salim Ali Altug, Luis Garcia +3
Let be a principally polarized abelian variety over a finite field with commutative endomorphism ring; further suppose that either is ordinary or the field is prime. Mo…
Green forms and the arithmetic Siegel-Weil formula
Luis E. Garcia, Siddarth Sankaran
We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1),…
Superconnections, theta series, and period domains
Luis E. Garcia
We use superconnections to define and study some natural differential forms on period domains that parametrize polarized Hodge structures of given type on a rational q…
Regularized theta lifts and (1,1)-currents on GSpin Shimura varieties. I
Luis E. Garcia
We introduce a regularized theta lift for reductive dual pairs of the form with a quadratic vector space over a totally real number field . The lift takes valu…
On the values of some singular currents on Shimura varieties of orthogonal type
Luis E. Garcia
In a previous paper (arxiv:1409.7353), we introduced a regularized theta lift for reductive dual pairs of the form with a quadratic vector space over a totally re…