Zeta-Functions of Varieties Over Finite Fields at s=1
Stephen Lichtenbaum · Birkhäuser Boston eBooks · 1983
Let κ be a finite field of cardinality q = p ’ . Let MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeaadaqdaaqaaiabeQ7aRbaaaaa!40E2! $$\overline \kappa $$ be a fixed algebraic closure of κ. Let X be a smooth projective algebraic variety of dimension d over κ such that MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbWexLMBbXgBd9gzLbvyNv2CaeHbl7mZLdGeaGqiVu0Je9sqqr % pepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs % 0-yqaqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaai % aabeqaamaabaabauaakeaadaqdaaqaaiaadIfaaaGaeyypa0Jaamiw % aiabgEna0oaanaaabaGaeqOUdSgaaaaa!45CA! $$\overline X = X \times \overline \kappa $$ is connected.