In this paper, we introduce GEMA, a genome exact mapping accelerator based on learned indexes, specifically designed for FPGA implementation. GEMA utilizes a machine learning (ML) algorithm to precisely locate the exact position of read sequences within the original sequence. To enhance the accuracy of the trained ML model, we incorporate data augmentation and data-distribution-aware partitioning techniques. Additionally, we present an efficient yet low-overhead error recovery technique. To map long reads more efficiently, we propose a speculative prefetching approach, which reduces the required memory bandwidth. Furthermore, we suggest an FPGA-based architecture for implementing the proposed mapping accelerator, optimizing the accesses to off-chip memory. Our studies demonstrate that GEMA achieves up to 1.36× higher speed for short reads compared to the corresponding results reported in recently published exact mapping accelerators. Moreover, GEMA achieves up to ∼22× faster mapping of long reads compared to the available results for the longest mapped reads using these accelerators.