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1089-11-370 Hilary Smallwood*, Department of Mathematics, Louis R. Weber Building, 841 Oval Drive, Fort Collins, CO 80523. Counting Abelian Surfaces with Real Multiplication over Fq . Preliminary report. Given a simple abelian surface, A/Fq , the endomorphism algebra, End(A) ⊗ Q contains a real quadratic subfield. For √ squarefree d > 0, we estimate the number of principally polarized abelian surfaces A/Fq such that Q( d) ⊂ End(A) ⊗ Q, and show that this quantity is approximately q 5/2 . (Received February 19, 2013) 1